This thesis describes the tertiary structures and dynamic studies of two protein systems. The first is human γC -crystallin protein, which is present in the nucleus of the human eye lens and the other is the plant viral protein VPg (an intrinsically disordered protein) in its free as well as its protease bound forms. The structural studies described here have been carried out using high-resolution solution NMR spectroscopic methods. Project I: Determination of solution structure and dynamics of Human γC-crystallin (HGC) using NMR spectroscopy The crystallins are the most abundant proteins in the eye lens of vertebrates. These proteins are packed in short-range spatial order to provide the transparency and appropriate refractive index gradient that are required for vision. The crystallins belong to two gene families, which are categorized as the alpha and beta/gamma crystallins respectively. The classification on the basis of molecular size and structure results in the proteins being referred to as alpha, beta and gamma crystallins. Again, each of the crystallins has two or more subtypes. The stoichiometry of the subtypes of α, β and γ crystallins varies with the age of the organism, but the order of abundance remains as β > α > γ irrespective of age. The most abundant crystallins in the nucleus (central region) of eye lens are the γ -crystallins. In the human lens, only three members of the γ− crystallin family are mainly expressed i.e. γS- (HGS), γC - (HGC) and γD - (HGD). HGS is expressed postnatally and thus is present mainly in the cortical region of the lens unlike HGC and HGD crystallins, which are present in the nucleus. It is known that aging and some cataract-associated genetic mutations alter the structure of these proteins. Other point mutations result in minimum structural perturbation but with drastically lowered solubility. Mutation in the human γC -crystallin leads to congenital cataract such as Coppock-like cataract, while structural information is available for HGD & HGS but no structure is available for HGC. However, recently a model structure has been reported for HGC based on a mouse orthologous. Based on this model structure, it was argued that HGC is an insoluble protein and was explained by lower magnitude of dipole moment and fluctuation in N-terminal domain of the model structure. However it is shown that HGC is very soluble protein. Solution structure of human γC-crystallin has been determined from an analysis of multidimensional triple resonance NMR spectroscopy using distance restraints from unambiguously assigned 1H-1H NOE peaks and dihedral angle restraints from HNHA and HNHB spectra. 15N relaxation average T1 and T2 correspond to 0.729 ± 0.02 and 0.060 ± 0.04 second from 15N backbone relaxation study, which gives average rotational correlation time 10.87 ns that shows human γC-crystallin is monomer in solution of molecular weight 21 kDa (173 residues). The ensemble of 20 lowest energy structures shows a root mean square deviation of 0.60 ± 0.12 Å for the backbone atoms, and 1.03 ± 0.09 Å for all heavy atoms. The comparison between the calculated NMR structure with backbone chain atoms C`, Cα and NH, of the x-ray crystal structure of the mouse γC - crystallin shows that the structure determined here of human γC-crystallin is very similar with an RMSD of 1.3 Å, which is not surprising given the 84.5% amino acid sequence identity between the two proteins. More importantly, the NMR structure reported here shows the subtle differences in the orientation of specific residues as well as the domain interface between the human and mouse orthologs. The orientation of the calculated dipole moment for this NMR structure differs from earlier reported for model structure. However it is similar to the other known soluble proteins. The determined solution structure of human γC-crystallin also enables us to estimate the effect of cataract-associative mutations on the structure and properties of the protein. Several such mutations are already known, and the work presented here could likely shed light on the molecular basis of these cataracts. Project II: Solution structural studies of intrinsically disordered protein VPg in free and bound forms from Sesbania mosaic virus Sesbania mosaic virus (SeMV) is a plant virus, which infects the Sesbania grandiflora tree. SeMV belongs to Sobemovirus genus, which is not defined under any family. The length of this viral genome is ~4kb. This viral genome has four open-reading frames (ORF). ORF1 and ORF2 encode movement and coat proteins, respectively. ORF2 is again split into two ORFs i.e. ORF2a and ORF2b by a -1 shift in the reading frame and encode two polypeptide chains. These polypeptide chains generate several functional proteins upon polyprotein processing. Polyprotein processing is a mechanism employed by animal and plant viruses to produce several functional proteins from a single polypeptide chain. The two polyproteins expressed are catalytically cleaved by a serine protease, thus releasing the four proteins: VPg (viral protein genome linked), RdRP (RNA dependent RNA polymerase), P10, and P8. VPg (“Viral Protein genome linked”) as its name suggests, is covalently linked to the 5` end of the viral RNA. VPgs are generally known to be intrinsically disordered proteins and have many interacting partners. Intrinsically Disordered Proteins (IDPs) are not explained by the 3D structure–function dogma. However, they are important for biological functions such as molecular recognition, signal transduction and regulation. It is known that SeMV protease becomes inactive in the absence of the VPg domain at its C-terminal. VPgs of animal viruses are well studied as compared to VPgs of plant virues. The size of VPg varies across the Sobemovirus genus. It is important to know the structure of VPg since it is necessary for protease activity. The studies conducted here focus on the structural analysis of the VPg in its free and bound forms with protease (VPg complex) as well as some aspect of full-length ProVPg. For structural studies, two constructs of VPg as fusion protein with Cytb5 tag, one lacking 23 residues at its C-terminal using the pET21a(+) plasmid vector have been designed. Sub-cloning was also done to add a thrombin recognition site to remove the hexa-His tag from new constructs of full-length ProVPg and protease (PRO). These proteins were highly expressed, isotopically labeled and purified for NMR study. The sample used for structural studies of the ProVPg 23 complex was prepared using selectively protonated Ile, Leu and Val; and isotopically labeled i.e. 2H, 13C, and 15N-VPg 23 protein. VPg in its free form is an intrinsically disordered protein and this has been confirmed by its dynamic nature observed using solution NMR spectroscopy. VPg binds to its partner protease and adopts a 3D-structure, which has been shown here. The tertiary structure has been determined using distance restraints from 1HN-1HN NOEs and methyl 1HN NOEs, and dihedral angle predicted from analysis of chemical shift values. The tertiary structure of ProVPg 23 complex has one β -sheet composed of three antiparallel β-strands and an α-helix. The ensemble of 20 lowest energy structures shows a root mean square deviation of 0.42 ± 0.09 Å for the backbone atoms, and 1.09 ± 0.11 Å for all heavy atoms for residues 15 to 50 that are primarily involved in structure formation. On the other hand RMSD is 2.34 ± 0.72 Å for the backbone and 2.55 ± 0.60 Å for all heavy atoms for all residues including both termini. That the tertiary fold of VPg both in full-length ProVPg and when complexed with protease domain (PRO) are the same has been shown here. The NMR structure reported here provides a structural basis for the origin of resonances in the up-field region of one–dimensional proton spectrum of full length ProVPg. The binding surface based on the structures of ProVPg 23 complex determined here and X-ray structure of PRO; has been determined using HADDOCK. The structural model here of full length ProVPg 23 shows the presence of aromatic interaction between Trp271 of PRO and Trp46 of VPg, which is consistent with the earlier biochemical studies.

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Knowledge of the dissociation constants of the ionizable protons of weak acids in aqueous media is of fundamental importance in many areas of chemistry and biochemistry. The pKa value, or equilibrium dissociation constant, of a molecule determines the relative concentration of its protonated and deprotonated forms at a specified pH and is therefore an important descriptor of its chemical reactivity. Considerable efforts have been devoted to the determination of pKa values by different experimental techniques. Although in most cases the determination of pKa values from experimental is straightforward, there are situations where interpretation is difficult and the results ambiguous. It is, therefore, not surprising that the capability to provide accurate estimates of the pKa value has been a central goal in theoretical chemistry and there has been a large effort in developing methodologies for predicting pKa values for a variety of chemical systems by differing quantum chemical techniques. A prediction accuracy within 0.5 pKa units of experiment is the desirable level of accuracy. This is a non-trivial exercise, for an error of 1 kcal/mol in estimates of the free energy value would result in an error of 0.74 pKa units. In this thesis ab initio Car-Parrinello molecular dynamics (CPMD) has been used for investigating the Brϕnsted acid-base chemistry of weak acids in aqueous solution. A key issue in any dissociation event is how the solvating water molecules arrange themselves spatially and dynamically around the neutral and dissociated acid molecule. Ab initio methods have the advantage that all solvent water molecules can, in principle, be con- sidered explicitly. One of the factors that has inhibited the widespread use of ab initio MD methods to study the dissociation reaction is that dissociation of weak acids are rare events that require extremely long simulation times before one is observed. The metady- namics formalism provides a solution to this conundrum by preventing the system from revisiting regions of configuration space where it has been in the past. The formalism allows the system to escape the free-energy minima by biasing the dynamics with a history dependent potential (or force) that acts on select degrees of freedom, referred to as collective variables. The bias potentials, modeled by repulsive inverted Gaussians that are dropped during propagation, drive the system out of any free-energy minima and allow it to explore the configurational space by a relatively quick and efficient sampling. The the- sis deals with a detailed investigation of the Brϕnsted acid-base chemistry of weak acids in aqueous solutions by the CPMD-metadynamics procedure. In Chapter 1, current approaches for the theoretical estimation of pKa values are summarized while in Chapter 2 the simulation methodology and the metadynamics sampling techniques used in this study are described. The potential of the CPMD-metadynamics procedure to provide estimates of the acid dissociation constant (pKa) is explored in Chapter 3, using acetic acid as a test sys- tem. Using the bond-distance dependent coordination number of protons bound to the dissociating carboxylic groups as the collective variable, the free-energy profile for the dissociation reaction of acetic acid in water was computed. Convergence of the free-energy profiles and barriers for the simulations parameters is demonstrated. The free-energy profiles exhibit two distinct minima corresponding to the dissociated and neutral states of the acid and the deterrence in their values provides the estimate for pKa. The estimated value of pKa for acetic acid from the simulations, 4.80, is in good agreement with the experiment at value of 4.76. It is shown that the good agreement with experiment is a consequence of the cancellation of errors, as the pKa values are computed as the divergence in the free energy values at the minima corresponding to the neutral and dissociated state. The chapter further explores the critical factors required for obtaining accurate estimates of the pKa values by the CPMD-metadynamics procedure. It is shown that having water molecules sufficient to complete three hydration shells as well as maintaining water density in the simulation cell as close to unity is important. In Chapter 4, the CPMD-metadynamics procedure described in Chapter-3 has been used to investigate the dissociation of a series of weak organic acids in aqueous solutions. The acids studied were chosen to highlight some of the major factors that influence the dissociation constant. These include the influence of the inductive effect, the stabilization of the dissociated anion by H-bonding as well as the presence of multiple ionizable groups. The acids investigated were aliphatic carboxylic acids, chlorine-substituted carboxylic acids, cis- and trans-butenedioic, the isomers of hydroxybenzoic acid and ophthalmic acids and its isomers. It was found that in each of these examples the CPMD-metadynamics procedure correctly estimates the pKa values, indicating that the formulism is capable of capturing these influences and equally importantly indicating that the cancellation of errors is indeed universal. Further, it is shown that the procedure can provide accurate estimates of the successive pKa values of polypro tic acids as well as the subtle difference in their values for different isomers of the acid molecule. Changes in protonation-deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. It is shown that CPMD simulations in conjunction with metadynamics calculations of the free energy profile of the protonation- deprotonation reaction can provide estimates of the multiple pKa values of the 20 canonical α-amino acids in aqueous solutions in good agreement with experiment (Chapter 5). The distance-dependent coordination number of the protons bound to the hydroxyl oxygen of the carboxylic and the amine groups is used as the collective variable to explore the free energy profiles of the Brϕnsted acid-base chemistry of amino acids in aqueous solutions. Water molecules, sufficient to complete three hydration shells surrounding the acid molecule were included explicitly in the computation procedure. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pKa values with a mean relative error with respect to experimental results, of 0.2 pKa units. The tripeptide Glutathione (GSH) is one of the most abundant peptides and the major repository for non-protein sulfur in both animal and plant cells. It plays a critical role in intracellular oxidative stress management by the reversible formation of glutathione disulfide with the thioldisulfide pair acting as a redox buffer. The state of charge of the ionizable groups of GSH can influences the redox couple and hence the pKa value of the cysteine residue of GSH is critical to its functioning. In Chapter 6, it has been reported that ab initio Car-Parrinello Molecular Dynamics simulations of glutathione solvated by 200 water molecules, all of which are considered in the simulation. It is shown that the free-energy landscape for the protonation - deprotonation reaction of the cysteine residue of GSH computed using metadynamics sampling provides accurate estimates of the pKa and correctly predicts the shift in the dissociation constant values as compared to the isolated cysteine amino acid. The dissociation constants of weak acids are commonly determined from pH-titration curves. For simple acids the determination of the pKa from the titration curves using the Henderson-Hasselbalch equation is relatively straightforward. There are situations, however, especially in polyprotic acids with closely spaced dissociation constants, where titration curves do not exhibit clear inflexion and equivalence stages and consequently the estimation of multiple pKa values from a single titration curve is no longer straightfor- ward resulting in uncertainties in the determined pKa values. In Chapter 7, the multiple dissociation constant of the hexapeptide glutathione disulfide (GSSG) with six ionizable groups and six associated dissociation constants has been investigated. The six pKa values of GSSG were estimated using the CPMD-metadynamics procedure from the free-energy profiles for each dissociation reaction computed using the appropriate collective variable. The six pKa values of GSSG were estimated and the theoretical pH-titration curve was then compared with the experimentally measured pH-titration curve and found to be in excellent agreement. The object of the exercise was to establish whether interpretation of pH-titration curves of complex molecules with multiple ionizable groups could be facilitated using results of ab initio molecular dynamics simulations.

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