|dc.description.abstract||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 deferent 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 conﬁguration 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 thisstudy 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 deference 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 diﬀerence 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, cid and trans-butenedioic, the isomers of hydroxybenzoic acid and phthalic 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 deference in their values for deterrent 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 polypro tic 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.||en_US