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Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can be associated with different characteristics of the orbits. The boundaries for these regions are clearly defined. Observational data can be directly associated with points in the regions. A possible extension of these considerations with an additional parameter for the case of Kerr geometry is briefly discussed.

Exact analytic expressions for planetary orbits and light trajectories in the Reissner-Nordstrom geometry are presented. They are characterized in a map specified by three dimensionless parameters for the planetary orbits, while two dimensionless parameters are required to map the trajectories of light. Notable differences with the corresponding orbits and trajectories in the Schwarzschild geometry are indicated. In particular, when the energy and angular momentum of the planet are fixed, the precession angle of the orbit decreases as the net electric charge of the massive star or black hole increases. A similar result also holds for the deflection angle of a light ray.

It is shown that the lowest order general relativistic correction produces elliptic orbits with a non-Newtonian eccentricity.

All possible orbital trajectories and their analytical expressions in the Schwarzschild metric are presented in a single complete map characterized by two dimensionless parameters. While three possible pairs of parameters with different advantages are described, the parameter space that gives the most convenient reduction to the Newtonian case is singled out and used which leads to a new insight on Newtonian limits among other results. Numerous analytic relations are presented. A comparison is made with the widely used formulation and presentation given by S. Chandrasekhar.

Some features of a parametrized space of orbits in the Schwarzschild geometry are described.

A new parameter space is used to classify circular orbits in the Schwarzschild metric.

Exact analytic expressions for various characteristics of the hyperbolic-type orbits of a particle in the Schwarzschild geometry are presented. A useful simple approximation formula is given for the case when the deviation from the Newtonian hyperbolic path is very small.

Tat is a transactivator of HIV transcription that can be secreted to affect nearby cells. Deleterious central nervous system effects of extracellular Tat include dopaminergic neuron dysfunction, raising the possibility that Tat secretion may be linked to Parkinsonian motor features seen in people with HIV (PWH). This study examined the potential association of anti-Tat antibodies and extrapyramidal motor dysfunction in PWH. In 42 PWH who were chronically infected and characterized for neurological abnormalities, anti-Tat IgG levels were lower in individuals with more severe extrapyramidal motor abnormalities as measured by the Unified Parkinson’s Disease Rating Scale (UPDRS). The association was observed specifically with IgG against the cysteine-rich Tat region. However, the IgG responses to Tat were weak in comparison to responses against the other HIV antigens. This disparity was evident in plasma and cerebrospinal fluid, and was also seen in early infection, before antiretroviral therapy. When the effects of antibodies on Tat function were evaluated, PWH plasma had no activity against Tat-induced transactivation, while Tat-immunized mouse and rabbit sera exhibited a potent inhibitory activity. These data provide initial evidence for a protective potential of anti-Tat antibodies and raise the possibility that a therapeutic Tat vaccine might alleviate clinical signs of HIV-associated dopaminergic dysfunction.

Antibodies are principal immune components elicited by vaccines to induce protection from microbial pathogens. In the Thai RV144 HIV-1 vaccine trial, vaccine efficacy was 31% and the sole primary correlate of reduced risk was shown to be vigorous antibody response targeting the V1V2 region of HIV-1 envelope. Antibodies against V3 also were inversely correlated with infection risk in subsets of vaccinees. Antibodies recognizing these regions, however, do not exhibit potent neutralizing activity. Therefore, we examined the antiviral potential of poorly neutralizing monoclonal antibodies (mAbs) against immunodominant V1V2 and V3 sites by passive administration of human mAbs to humanized mice engrafted with CD34+ hematopoietic stem cells, followed by mucosal challenge with an HIV-1 infectious molecular clone expressing the envelope of a tier 2 resistant HIV-1 strain. Treatment with anti-V1V2 mAb 2158 or anti-V3 mAb 2219 did not prevent infection, but V3 mAb 2219 displayed a superior potency compared to V1V2 mAb 2158 in reducing virus burden. While these mAbs had no or weak neutralizing activity and elicited undetectable levels of antibody-dependent cellular cytotoxicity (ADCC), V3 mAb 2219 displayed a greater capacity to bind virus- and cell-associated HIV-1 envelope and to mediate antibody-dependent cellular phagocytosis (ADCP) and C1q complement binding as compared to V1V2 mAb 2158. Mutations in the Fc region of 2219 diminished these effector activities in vitro and lessened virus control in humanized mice. These results demonstrate the importance of Fc functions other than ADCC for antibodies without potent neutralizing activity.

Immune complexes (ICs) made of antibody-bound antigens exhibit immunomodulatory activities exploitable in a vaccination strategy to optimize vaccine efficacy. The modulatory effects of ICs are typically attributed to the Fc fragments of the antibody components, which engage Fc receptors, complement and complement receptors on various immune cells. These Fc-mediated functions facilitate the critical interplay between innate and adaptive immune systems to impact the quality and quantity of the elicited adaptive responses. In addition to the Fc contribution, the Fab fragment also plays an immunoregulation role. The antigen-binding domains of the Fab fragment can bind their specific epitopes at high affinity to sterically occlude these antigenic sites from recognition by other antibodies. Moreover, the Fab-mediated binding has been demonstrated to induce allosteric alterations at nearby or distant antigenic sites. In this review article, we survey published studies to illuminate how the immunomodulatory functions of ICs have been investigated or utilized in a vaccination strategy to fight against an array of infectious pathogens, culminating with IC vaccine designs aimed at preventing HIV-1 infection. In particular, we highlight IC vaccine candidates that exploit Fab-mediated steric and allosteric effects to direct antibody responses away or toward the V1V2 domain, the V3 loop, and other antigenic sites on the HIV-1 envelope gp120 glycoprotein. Like other HIV-1 vaccine approaches, the path for IC-based vaccines to reach the clinic faces major hurdles yet to be overcome; however, investigations into this vaccine strategy have provided insights into the multifaceted activities of antibodies beyond their conventional roles in the host defense against HIV-1 and other microbial pathogens.