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Vaccination strategies aimed at maturing broadly neutralizing antibodies (bnAbs) from naïve precursors are hindered by unusual features that characterize these Abs, including insertions and deletions (indels). Longitudinal studies of natural HIV infection cases shed light on the complex processes underlying bnAb development and have suggested a role for superinfection as a potential enhancer of neutralization breadth. Here we describe the development of a potent bnAb lineage that was elicited by two founder viruses to inform vaccine design. The V3-glycan targeting bnAb lineage (PC39-1) was isolated from subtype C-infected IAVI Protocol C elite neutralizer, donor PC39, and is defined by the presence of multiple independent insertions in CDRH1 that range from 1-11 amino acids in length. Memory B cell members of this lineage are predominantly atypical in phenotype yet also span the class-switched and antibody-secreting cell compartments. Development of neutralization breadth occurred concomitantly with extensive recombination between founder viruses before each virus separated into two distinct population "arms" that evolved independently to escape the PC39-1 lineage. Ab crystal structures show an extended CDRH1 that can help stabilize the CDRH3. Overall, these findings suggest that early exposure of the humoral system to multiple related Env molecules could promote the induction of bnAbs by focusing Ab responses to conserved epitopes.

In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is considered. A connection with the coupled dispersionless equation and Mannheim curve pair is established. Also, the Lax pair of the obtained coupled dispersionless equation from the motions of any Mannheim curve pair is given. This gives us a significant condition based on the curvature and torsion of any Mannheim curve for its integrability since it is well-known that the Lax pair provides the integrability of di erential equations.

Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic curves in 3 and 4-dimensional Euclidean spaces have been considered and the motions of inextensible quaternionic curves have been characterized by the modified Korteweg-de Vries (mKdV) equations. For this purpose, the basic concepts of the quaternions and quaternionic curves have been summarized. Then the evolutions of inextensible quaternionic curves with reference to the Frenet formulae have been obtained. Finally, the mKdV equations have been generated with the help of their evolutions

Understanding how broadly neutralizing antibodies (bnAbs) to HIV envelope (Env) develop during natural infection can help guide the rational design of an HIV vaccine. Here, we described a bnAb lineage targeting the Env V2 apex and the Ab-Env co-evolution that led to development of neutralization breadth. The lineage Abs bore an anionic heavy chain complementarity-determining region 3 (CDRH3) of 25 amino acids, among the shortest known for this class of Abs, and achieved breadth with only 10% nucleotide somatic hypermutation and no insertions or deletions. The data suggested a role for Env glycoform heterogeneity in the activation of the lineage germline B cell. Finally, we showed that localized diversity at key V2 epitope residues drove bnAb maturation toward breadth, mirroring the Env evolution pattern described for another donor who developed V2-apex targeting bnAbs. Overall, these findings suggest potential strategies for vaccine approaches based on germline-targeting and serial immunogen design.

In this paper, we introduce the dual magnetic trajectories traced by the dual Frenet vectors of any dual curves in dual space via the dual Lorentz force, and then we give the characterizations of dual magnetic curves. Moreover, we define the dual flux ruled surfaces corresponding to the Killing vectors on the dual unit sphere and identify the conditions for these surfaces to be minimal or developable. Additionally, we present certain characterizations related to these surfaces. We demonstrate the visual representations of some dual flux ruled surfaces in some examples. [ABSTRACT FROM AUTHOR]

In this study, constant angle ruled surfaces with a pointwise 1-type Gauss map, which is very useful in the classification of surfaces, are investigated in terms of the Frenet elements of the base curves of the ruled surfaces in Euclidean 3-space. In order to form a basis for our work, firstly, basic concepts related to the Gauss map of an oriented surface are given. Later, a classification is satisfied by determining the necessary conditions to be the first kind, the second kind, and the harmonic of the pointwise 1-type of the Gauss map for these surfaces. Finally, some examples of these surfaces are provided, and their graphical illustrations are displayed. [ABSTRACT FROM AUTHOR]

The ability to study rapidly evolving viral populations has been constrained by the read length of next-generation sequencing approaches and the sampling depth of single-genome amplification methods. Here, we develop and characterize a method using Pacific Biosciences' Single Molecule, Real-Time (SMRT®) sequencing technology to sequence multiple, intact full-length human immunodeficiency virus-1 env genes amplified from viral RNA populations circulating in blood, and provide computational tools for analyzing and visualizing these data.

The ability to study rapidly evolving viral populations has been constrained by the read length of next-generation sequencing approaches and the sampling depth of single-genome amplification methods. Here, we develop and characterize a method using Pacific Biosciences' Single Molecule, Real-Time (SMRT®) sequencing technology to sequence multiple, intact full-length human immunodeficiency virus-1 env genes amplified from viral RNA populations circulating in blood, and provide computational tools for analyzing and visualizing these data.

We present BUSTED, a new approach to identifying gene-wide evidence of episodic positive selection, where the non-synonymous substitution rate is transiently greater than the synonymous rate. BUSTED can be used either on an entire phylogeny (without requiring an a priori hypothesis regarding which branches are under positive selection) or on a pre-specified subset of foreground lineages (if a suitable a priori hypothesis is available). Selection is modeled as varying stochastically over branches and sites, and we propose a computationally inexpensive evidence metric for identifying sites subject to episodic positive selection on any foreground branches. We compare BUSTED with existing models on simulated and empirical data. An implementation is available on www.datamonkey.org/busted, with a widget allowing the interactive specification of foreground branches.

In this study, we investigate the condition that a given polynomial curve with respect to the Frenet like curve (Flc) frame is a Tzitzeica curve. We also show that any planar polynomial curve cannot be a Tzitzeica curve. Finally, the condition to be the Tzitzeica curve for each of the spherical indicatrix curves defined according to the Flc frame is expressed, separately. [ABSTRACT FROM AUTHOR]

In this study, we investigate the geometric and algebraic aspects of defocusing Complex Coupled Dispersionless (CCD) equations in Minkowski space. We give the conditions for obtaining CCD equations from moving spacelike or timelike space curves using the Frenet and Darboux frames. Besides, we present the Lax pairs that indicate that the corresponding CCD equations are integrable. Finally, we evaluate the conserved quantities for CCD equations from the geometric point of view. [ABSTRACT FROM AUTHOR]

Spinors play a fundamental role in geometry and physics. The Clifford algebra is the natural linear algebraic setting where spinors and spin groups are formulated. In this study, spinors, which have many uses in Clifford algebras, have been given with a different representation in E3. Firstly, the directional q -frame has been considered, and this frame is represented with a spinor in spinor space. Later, considering the relations between the directional q -frame and Frenet frame, the relations between spinors corresponding to these frames have been obtained. In this way, a different construction of the spinors by using in Clifford algebras has been shown. [ABSTRACT FROM AUTHOR]

In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to the Frenet vectors of non-null space curves, are introduced with extra conditions that guarantee the existence of definite surface normals. First, the requirements of each pair of partner-ruled surfaces to be simultaneously developable and minimal (or maximal for spacelike surfaces) are investigated. The surfaces also simultaneously characterize the asymptotic, geodesic and curvature lines of the parameter curves of these surfaces. Finally, the study provides examples of timelike and spacelike partner-ruled surfaces and includes their graphs. [ABSTRACT FROM AUTHOR]

Monoclonal antibody 10-1074 targets the V3 glycan supersite on the HIV-1 envelope (Env) protein. It is among the most potent anti-HIV-1 neutralizing antibodies isolated so far. Here we report on its safety and activity in 33 individuals who received a single intravenous infusion of the antibody. 10-1074 was well tolerated and had a half-life of 24.0 d in participants without HIV-1 infection and 12.8 d in individuals with HIV-1 infection. Thirteen individuals with viremia received the highest dose of 30 mg/kg 10-1074. Eleven of these participants were 10-1074-sensitive and showed a rapid decline in viremia by a mean of 1.52 log[sub.10] copies/ml. Virologic analysis revealed the emergence of multiple independent 10-1074-resistant viruses in the first weeks after infusion. Emerging escape variants were generally resistant to the related V3-specific antibody PGT121, but remained sensitive to antibodies targeting nonoverlapping epitopes, such as the anti-CD4-binding-site antibodies 3BNC117 and VRC01. The results demonstrate the safety and activity of 10-1074 in humans and support the idea that antibodies targeting the V3 glycan supersite might be useful for the treatment and prevention of HIV-1 infection., Author(s): Marina Caskey (corresponding author) [1]; Till Schoofs [1]; Henning Gruell [2, 3, 4]; Allison Settler [1]; Theodora Karagounis [1]; Edward F Kreider [5]; Ben Murrell [6]; Nico Pfeifer [7]; [...]