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.

The humoral response to HIV-1: new insights, renewed focus.

During the past 2 decades, significant advances in our understanding of the humoral immune response to human immunodeficiency virus type 1 (HIV-1) infection have been made, yet a tremendous amount of work lies ahead. Despite these advances, strategies to reliably induce antibodies that can control HIV-1 infection are still critically needed. However, recent advances in our understanding of the kinetics, specificity, and function of early humoral responses offer alternative new approaches to attain this goal. These results, along with the new broadly neutralizing antibody specificities, the role for other antibody functions, the increased understanding of HIV-1-induced changes to B cell biology, and results from the RV144 "Thai" trial showing potential modest sterilizing protection by nonneutralizing antibody responses, have renewed focus on the humoral system. In this review, recent advances in our understanding of the earliest humoral responses are discussed, highlighting presentations from the meeting on the Biology of Acute HIV Infection.

HIV-1 envelope gp41 antibodies can originate from terminal ileum B cells that share cross-reactivity with commensal bacteria.

Monoclonal antibodies derived from blood plasma cells of acute HIV-1-infected individuals are predominantly targeted to the HIV Env gp41 and cross-reactive with commensal bacteria. To understand this phenomenon, we examined anti-HIV responses in ileum B cells using recombinant antibody technology and probed their relationship to commensal bacteria. The dominant ileum B cell response was to Env gp41. Remarkably, a majority (82%) of the ileum anti-gp41 antibodies cross-reacted with commensal bacteria, and of those, 43% showed non-HIV-1 antigen polyreactivity. Pyrosequencing revealed shared HIV-1 antibody clonal lineages between ileum and blood. Mutated immunoglobulin G antibodies cross-reactive with both Env gp41 and microbiota could also be isolated from the ileum of HIV-1 uninfected individuals. Thus, the gp41 commensal bacterial antigen cross-reactive antibodies originate in the intestine, and the gp41 Env response in HIV-1 infection can be derived from a preinfection memory B cell pool triggered by commensal bacteria that cross-react with Env.

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.

Isolation of HIV-1-neutralizing mucosal monoclonal antibodies from human colostrum.

BACKGROUND: Generation of potent anti-HIV antibody responses in mucosal compartments is a potential requirement of a transmission-blocking HIV vaccine. HIV-specific, functional antibody responses are present in breast milk, and these mucosal antibody responses may play a role in protection of the majority of HIV-exposed, breastfeeding infants. Therefore, characterization of HIV-specific antibodies produced by B cells in milk could guide the development of vaccines that elicit protective mucosal antibody responses. METHODS: We isolated B cells from colostrum of an HIV-infected lactating woman with a detectable neutralization response in milk and recombinantly produced and characterized the resulting HIV-1 Envelope (Env)-specific monoclonal antibodies (mAbs). RESULTS: The identified HIV-1 Env-specific colostrum mAbs, CH07 and CH08, represent two of the first mucosally-derived anti-HIV antibodies yet to be reported. Colostrum mAb CH07 is a highly-autoreactive, weakly-neutralizing gp140-specific mAb that binds to linear epitopes in the gp120 C5 region and gp41 fusion domain. In contrast, colostrum mAb CH08 is a nonpolyreactive CD4-inducible (CD4i) gp120-specific mAb with moderate breadth of neutralization. CONCLUSIONS: These novel HIV-neutralizing mAbs isolated from a mucosal compartment provide insight into the ability of mucosal B cell populations to produce functional anti-HIV antibodies that may contribute to protection against virus acquisition at mucosal surfaces.

Mapping the semantic structure of cognitive neuroscience.

Cognitive neuroscience, as a discipline, links the biological systems studied by neuroscience to the processing constructs studied by psychology. By mapping these relations throughout the literature of cognitive neuroscience, we visualize the semantic structure of the discipline and point to directions for future research that will advance its integrative goal. For this purpose, network text analyses were applied to an exhaustive corpus of abstracts collected from five major journals over a 30-month period, including every study that used fMRI to investigate psychological processes. From this, we generate network maps that illustrate the relationships among psychological and anatomical terms, along with centrality statistics that guide inferences about network structure. Three terms--prefrontal cortex, amygdala, and anterior cingulate cortex--dominate the network structure with their high frequency in the literature and the density of their connections with other neuroanatomical terms. From network statistics, we identify terms that are understudied compared with their importance in the network (e.g., insula and thalamus), are underspecified in the language of the discipline (e.g., terms associated with executive function), or are imperfectly integrated with other concepts (e.g., subdisciplines like decision neuroscience that are disconnected from the main network). Taking these results as the basis for prescriptive recommendations, we conclude that semantic analyses provide useful guidance for cognitive neuroscience as a discipline, both by illustrating systematic biases in the conduct and presentation of research and by identifying directions that may be most productive for future research.

Interrogation of individual intratumoral B lymphocytes from lung cancer patients for molecular target discovery.

Intratumoral B lymphocytes are an integral part of the lung tumor microenvironment. Interrogation of the antibodies they express may improve our understanding of the host response to cancer and could be useful in elucidating novel molecular targets. We used two strategies to explore the repertoire of intratumoral B cell antibodies. First, we cloned VH and VL genes from single intratumoral B lymphocytes isolated from one lung tumor, expressed the genes as recombinant mAbs, and used the mAbs to identify the cognate tumor antigens. The Igs derived from intratumoral B cells demonstrated class switching, with a mean VH mutation frequency of 4%. Although there was no evidence for clonal expansion, these data are consistent with antigen-driven somatic hypermutation. Individual recombinant antibodies were polyreactive, although one clone demonstrated preferential immunoreactivity with tropomyosin 4 (TPM4). We found that higher levels of TPM4 antibodies were more common in cancer patients, but measurement of TPM4 antibody levels was not a sensitive test for detecting cancer. Second, in an effort to focus our recombinant antibody expression efforts on those B cells that displayed evidence of clonal expansion driven by antigen stimulation, we performed deep sequencing of the Ig genes of B cells collected from seven different tumors. Deep sequencing demonstrated somatic hypermutation but no dominant clones. These strategies may be useful for the study of B cell antibody expression, although identification of a dominant clone and unique therapeutic targets may require extensive investigation.

A Therapeutic Antibody for Cancer, Derived from Single Human B Cells.

Some patients with cancer never develop metastasis, and their host response might provide cues for innovative treatment strategies. We previously reported an association between autoantibodies against complement factor H (CFH) and early-stage lung cancer. CFH prevents complement-mediated cytotoxicity (CDC) by inhibiting formation of cell-lytic membrane attack complexes on self-surfaces. In an effort to translate these findings into a biologic therapy for cancer, we isolated and expressed DNA sequences encoding high-affinity human CFH antibodies directly from single, sorted B cells obtained from patients with the antibody. The co-crystal structure of a CFH antibody-target complex shows a conformational change in the target relative to the native structure. This recombinant CFH antibody causes complement activation and release of anaphylatoxins, promotes CDC of tumor cell lines, and inhibits tumor growth in vivo. The isolation of anti-tumor antibodies derived from single human B cells represents an alternative paradigm in antibody drug discovery.

Maternal HIV-1 envelope-specific antibody responses and reduced risk of perinatal transmission.

Despite the wide availability of antiretroviral drugs, more than 250,000 infants are vertically infected with HIV-1 annually, emphasizing the need for additional interventions to eliminate pediatric HIV-1 infections. Here, we aimed to define humoral immune correlates of risk of mother-to-child transmission (MTCT) of HIV-1, including responses associated with protection in the RV144 vaccine trial. Eighty-three untreated, HIV-1-transmitting mothers and 165 propensity score-matched nontransmitting mothers were selected from the Women and Infants Transmission Study (WITS) of US nonbreastfeeding, HIV-1-infected mothers. In a multivariable logistic regression model, the magnitude of the maternal IgG responses specific for the third variable loop (V3) of the HIV-1 envelope was predictive of a reduced risk of MTCT. Neutralizing Ab responses against easy-to-neutralize (tier 1) HIV-1 strains also predicted a reduced risk of peripartum transmission in secondary analyses. Moreover, recombinant maternal V3-specific IgG mAbs mediated neutralization of autologous HIV-1 isolates. Thus, common V3-specific Ab responses in maternal plasma predicted a reduced risk of MTCT and mediated autologous virus neutralization, suggesting that boosting these maternal Ab responses may further reduce HIV-1 MTCT.

Latent Space and Social Psychological Models of Diffusion

The problem of social diffusion has animated sociological thinking on topics ranging from the spread of an idea, an innovation or a disease, to the foundations of collective behavior and political polarization. While network diffusion has been a productive metaphor, the reality of diffusion processes is often muddier. Ideas and innovations diffuse differently from diseases, but, with a few exceptions, the diffusion of ideas and innovations has been modeled under the same assumptions as the diffusion of disease. In this dissertation, I develop two new diffusion models for "socially meaningful" contagions that address two of the most significant problems with current diffusion models: (1) that contagions can only spread along observed ties, and (2) that contagions do not change as they spread between people. I augment insights from these statistical and simulation models with an analysis of an empirical case of diffusion - the use of enterprise collaboration software in a large technology company. I focus the empirical study on when people abandon innovations, a crucial, and understudied aspect of the diffusion of innovations. Using timestamped posts, I analyze when people abandon software to a high degree of detail.

To address the first problem, I suggest a latent space diffusion model. Rather than treating ties as stable conduits for information, the latent space diffusion model treats ties as random draws from an underlying social space, and simulates diffusion over the social space. Theoretically, the social space model integrates both actor ties and attributes simultaneously in a single social plane, while incorporating schemas into diffusion processes gives an explicit form to the reciprocal influences that cognition and social environment have on each other. Practically, the latent space diffusion model produces statistically consistent diffusion estimates where using the network alone does not, and the diffusion with schemas model shows that introducing some cognitive processing into diffusion processes changes the rate and ultimate distribution of the spreading information. To address the second problem, I suggest a diffusion model with schemas. Rather than treating information as though it is spread without changes, the schema diffusion model allows people to modify information they receive to fit an underlying mental model of the information before they pass the information to others. Combining the latent space models with a schema notion for actors improves our models for social diffusion both theoretically and practically.

The empirical case study focuses on how the changing value of an innovation, introduced by the innovations' network externalities, influences when people abandon the innovation. In it, I find that people are least likely to abandon an innovation when other people in their neighborhood currently use the software as well. The effect is particularly pronounced for supervisors' current use and number of supervisory team members who currently use the software. This case study not only points to an important process in the diffusion of innovation, but also suggests a new approach -- computerized collaboration systems -- to collecting and analyzing data on organizational processes.