The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different three-body systems are considered, the main concern of the investigation being the i) calculation of binding energies for weakly bounded trimers, ii) handling of systems with a plethora of states, iii) importance of three-body forces in trimers, and iv) the development of a numerical technique for reliably handling three-dimensional integrodifferential equations. In this respect we considered the three-body nuclear problem, the 4He trimer, and the Ozone (16 0 3 3) system. In practice, we solve the three-dimensional equations using the orthogonal collocation method with triquintic Hermite splines. The resulting eigenvalue equation is handled using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics)

The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different three-body systems are considered, the main concern of the investigation being the i) calculation of binding energies for weakly bounded trimers, ii) handling of systems with a plethora of states, iii) importance of three-body forces in trimers, and iv) the development of a numerical technique for reliably handling three-dimensional integrodifferential equations. In this respect we considered the three-body nuclear problem, the 4He trimer, and the Ozone (16 0 3 3) system. In practice, we solve the three-dimensional equations using the orthogonal collocation method with triquintic Hermite splines. The resulting eigenvalue equation is handled using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics)

A number of viral diseases such as Hepatitis B, small pox, measles, rubella and polio have effective vaccines to control or eradicate them. HIV-1 is a lentivirus which infects human immune cells and leads to the disease called AIDS (Acquired Immuno Deficiency Syndrome). Despite much effort since the three decades of its discovery, there is no effective vaccine against HIV-1. The envelope glycoprotein of HIV-1 is the most accessible protein on the virion surface and is essential for HIV-1 infection. Thus, this protein is the primary target for HIV-1 vaccine design. However, HIV-1 has acquired numerous immune evasive mechanisms to escape from the human immune system. Various factors such as high variability of the envelope sequence, presence of immune dominant variable loop regions, extensive glycosylation which masks conserved epitopes on the envelope, weak non-covalent interactions between gp120 and gp41 subunits of the envelope and the metastable nature of the envelope hinder the development of an effective vaccine against HIV-1. Various approaches have been carried out to design immunogens based on the envelope glycoprotein but so far none of these have succeeded in elicitation of a broad neutralizing antibody response. In chapter 1, brief descriptions of the HIV-1 epidemic, structural and genomic organization of HIV-1 along with the difficulties faced and progress in the development of an HIV-1 vaccine are described. HIV-1 envelope glycoprotein (Env) is a trimer of gp120-gp41 heterodimers. The gp41 subunit in the native, pre-fusion trimeric Env exists in a metastable conformation and attains a stable post-fusion six helix bundle (6HB) conformation comprised of a trimer of N-heptad repeat (NHR) and C-heptad repeat (CHR) heterodimers, that drives fusion of viral and cellular membranes. The metastable nature of gp41 drives the equilibrium towards the post-fusion conformation which favours shedding of gp120 and formation of the gp41 six helix bundle remnants from the Env trimer. These dissociated products display non-neutralizing epitopes to the immune system to drive non-neutralizing antibody responses. Design and purification of Env glycoprotein in its native trimeric form is challenging due to the instability of the functional HIV-1 native Env trimer. In chapter 2, we describe our attempts to stabilize native Env trimers by incorporation of mutations at the NHR:CHR interface that disrupt the post-fusion 6HB of gp41. The mutations V570D and I573D stabilize native JRFL Env and occlude non-neutralizing epitopes to a greater extent than the previously identified I559P mutation that it is at the interface of the NHR trimers in the 6HB. The mutations prevent sCD4 induced gp120 shedding and 6HB formation. The data suggest that positions 570 and 573 are surface proximal in the native Env. Aspartic acid substitutions at these positions stabilize native trimers through destabilization of the post fusion 6HB conformation. These mutations should enhance the exposure of native Env forms to the immune system and therefore can be used to stabilize Env in a DNA vaccine format. In previous studies, a disulfide bond was engineered between gp120 and gp41 of Env to stabilize the interactions between them (SOS gp140). An I559P mutation was also introduced to stabilize the native gp41 conformation in the context of disulfide engineered Env (SOSIP gp140). The purified, soluble SOSIP gp140 immunogens were trimeric and cleaved properly. However, these immunogens failed to elicit broad neutralizing responses. The SOSIP gp140 immunogens appear to be good conformational mimics of the native trimeric Env. Thus, it is important to understand the details of the conformation and antigenic nature of SOSIP Env to further assist the design of Env immunogens in a native-like conformation. In chapter 3, we expressed JRFL-SOSIP Env on the cell surface and probed with various gp120 and gp41 specific antibodies to investigate whether this Env protein mimics the native like Env conformation. We show that introduction of a disulfide bond between gp120 and gp41 perturbs the native Env conformation, though this effect is partially alleviated by furin expression. The introduction of the V570D mutation instead of the I559P mutation partially restored the native like conformation of disulfide engineered Env. Proper cleavage of the Env to gp120 and gp41 is essential for the formation of native Env conformation. Uncleaved Env attains non-native forms and binds to non-neutralizing antibodies. To overcome inefficient cleavage problems, we co-expressed gp120 and gp41 genes on separate plasmids in mammalian cells and monitored the formation of native like Env complexes on the cell surface. We observed a fraction of native-like Env complexes on the cell surface when gp120 and gp41 with the V570D mutation are co¬expressed. We also describe the expression of Env with a self-cleavable 2A peptide between gp120 and gp41-V570D. We conclude that co-expression of gp120 and gp41 to form native like Env complexes is possible. HIV-1 Env trimeric immunogens are believed to be better immunogens than monomeric gp120. The trimeric Env immunogens designed so far, elicited marginally better neutralizing antibody response than monomeric gp120. However, these immunogens failed to elicit antibodies which could neutralize multiple primary HIV-1 isolates. Thus, it is possible that these immunogens have failed to mimic the native Env conformation. Cryo-EM and crystal structures of Env suggested that three gp120 monomers are held together at the apex of the Env trimer and the V1V2 regions of each gp120 monomer contribute to this trimeric interface. It was also shown that two broadly neutralizing antibodies (PG9 and PG16) bind to quaternary epitopes formed by V1V2 regions. Based on these observations, we hypothesized that insertion of heterologous trimerization domains into V1V2 loops might help in the formation of native like gp120 trimers. In chapter 4, two different trimerization domains (6-helix bundle and foldon trimerization domains) were inserted at the V1 loop of gp120 and C1 and C5 regions of gp120 were deleted to reduce the conformational flexibility of gp120. The resulting constructs were not trimeric and lost binding to trimer specific antibodies, PG9 and PG16. Due to their large distances between N and C-termini, these trimerization domains might have altered the local conformation of V1V2 regions and destabilized gp120 trimer formation. Interestingly, introduction of a trimerization domain (hCMP) at the C-terminus of C1 and C5 deleted gp120 (gp120-hCMP-21), led to the formation of native-like trimers which bound to both PG9 and PG16 antibodies. These results suggest that it may be difficult to trimerize gp120 by insertion of heterologous trimerization domains into the V1V2 loop and that conformational integrity of the V1V2 region is essential for the formation of trimeric gp120 interface. V1V2 regions of gp120 form quaternary epitopes on the Env trimer and are target for several broadly neutralizing antibodies. Moreover, these regions are important for the formation of the gp120 trimeric interface in the Env. In chapter 4, we show that insertion of heterologous trimerization domains at the V1 loop failed to form native like gp120 trimers. To further investigate this issue, in chapter 5, we made cyclic permutants of the gp120 molecule to create new N and C-termini at the V1 or V2 loop regions. This allowed the insertion of heterologous trimerization domains at these loop regions without affecting the folding and stability of gp120. The hCMP trimerization domain was introduced at the N-terminus of cyclically permuted gp120 (V1cyc and V2cyc). The resulting cyclic permutants were trimeric and retained binding to several broadly neutralizing antibodies. These cyclic permutants showed 10-20 fold increased binding to quaternary epitope specific neutralizing antibodies PG9 and PGT 145. CD4 binding site directed broadly neutralizing antibodies b12 and VRC01 also showed increased affinities to these cyclic permutants. Immunization of guinea pigs with cyclic permutants elicited broad neutralizing antibody response to Tier-1 and Tier-2 HIV-1 isolates with substantially higher titers than the corresponding monomeric gp120 immunogens. The data demonstrate that cyclic permutation of gp120 did not affect the structural and functional properties of gp120. It is possible to elicit broadly neutralizing sera against HIV-1 using cyclically permuted gp120 trimers in small animals. Among several proposed cryo-EM tomography structures of trimeric Env, some suggested that the V1V2 loop regions of gp120 are located close to the trimer interface while some other structures suggested that the V1V2 loop regions of gp120 are located far from the trimer axis. The present study supports Env models in which the V1V2 loops are proximal to the trimer interface. This has recently been confirmed in high resolution cryo-EM and crystal structures of HIV-1 gp140 derivatives. HIV-1 Env subunit gp120 has 50% of its molecular mass comprised of glycans which shield Env from immune recognition. Env has approximately 25 glycosylation sites of which ~4 are located in the inner domain, ~7-8 in the V1/V2 and V3 loops and the rest in the outer domain (OD). Earlier reports suggested that the glycans are indispensable for proper folding of Env and a certain level of glycan coverage is essential for maintaining infectivity of the virion. In chapter 6, we investigated the effect of removal of glycans from core gp120 on the infectivity of the HIV-1 and on the recognition of Env by various broadly neutralizing antibodies (bNAbs). We mutated the glycosylation sites in core gp120 to the second most frequent amino acids based on multiple sequence alignment. Pseudoviral infectivity assays and mammalian cell surface display experiments show that in the context of gp160, all core gp120 glycans are dispensable for viral infectivity and for recognition of bNAbs. We also show that deglycosylated molecules can serve as a starting point to re-introduce epitopes for specific glycan dependent bNAbs. Several of the constructs will also be useful for epitope mapping and Env structural characterization. Glycosylation of Env is known to inhibit binding to germline precursors of known bNAbs. In this study we show that recognition of VRC01 germline-bNAb increases substantially with the progressive loss of glycans from JRFL pseudoviruses. This work has so far resulted in the following publications (mentioned in next page).