Determination of the Reaction Coordinate for a Key Conformational Fluctuation in Human Carbonic Anhydrase II

1H, 15N and13C resonance assignments of S2A mutant of human carbonic anhydrase II

In preparation for a detailed exploration of the structural and functional aspects of the Ser2Ala mutant of human carbonic anhydrase II, we present here almost complete sequence-specific resonance assignments for 1H, 15N, and 13C. The mutation of serine to alanine at position 2, located in the N-terminal region of the enzyme, significantly alters the hydrophilic nature of the site, rendering it hydrophobic. Consequently, there is an underlying assumption that this mutation would repel water from the site. However, intriguingly, comparative analysis of the mutant structure with the wild type reveals minimal discernible differences. These assignments serve as the basis for in-depth studies on histidine dynamics, protonation states, and its intricate role in protein-water interactions and catalysis.

pH-Dependent Structure and Dynamics of the Catalytic Domains of Human Carbonic Anhydrase II and IX

Extensive computer simulation studies have been carried out to probe the pH-dependent structure and dynamics of the two most efficient isoenzymes II and IX of human carbonic anhydrase (HCA) that control the pH in the human body. The equilibrium structure and hydration of their catalytic domains are found to be largely unaffected by the variation of pH in the range studied, in close agreement with the known experimental results. In contrast, a significant effect of the change in pH is observed for the first time on the local electrostatic potential of the active site walls and the dynamics of active site water molecules. We also report for the first time the free energy and kinetics of coupled fluctuations of orientation and protonation states of the well-known His-mediated proton shuttle (His-64) in both isozymes at pH 7 and 8. The transitions between different tautomers of in or out conformations of His-64 side chain range between 109 and 106 s-1 depending on pH. Possible implications of these results on conformation-dependent pKa of His-64 side chain and its role in driving the catalysis toward hydration of CO2 or dehydration of HCO3- with varying pH are discussed.

Diffusion in a two-dimensional energy landscape in the presence of dynamical correlations and validity of random walk model

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and it also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and simulations of a tagged particle moving on a two-dimensional periodic potential energy surface, both in the presence and absence of noise. Langevin dynamics simulations at multiple temperatures are carried out to obtain the diffusion coefficient of a solute particle. Friction is varied from zero to large values. Diffusive motion emerges in the limit of a long time, even in the absence of noise. Noise destroys the correlations and increases diffusion at small friction. Diffusion thus exhibits a nonmonotonic friction dependence at the intermediate value of the damping, ultimately converging to our theoretically predicted value. The latter is obtained using the well-established relationship between diffusion and random walk. An excellent agreement is obtained between theory and simulations in the high-friction limit but not so in the intermediate regime. We explain the deviation in the low- to intermediate-friction regime using the modified random walk theory. The rate of escape from one cell to another is obtained from the multidimensional rate theory of Langer. We find that enhanced dimensionality plays an important role. To quantify the effects of noise on the potential-imposed coherence on the trajectories, we calculate the Lyapunov exponent. At small friction values, the Lyapunov exponent mimics the friction dependence of the rate.

Structure and Dynamics of the Isozymes II and IX of Human Carbonic Anhydrase

Human carbonic anhydrases (HCAs) are responsible for the pH control and sensing in our body and constitute key components in the central pH paradigm connected to cancer therapeutics. However, little or no molecular level studies are available on the pH-dependent stability and functional dynamics of the known isozymes of HCA. The main objective of this Article is to report the first bench-marking study on the structure and dynamics of the two most efficient isozymes, HCA II and IX, at neutral pH using classical molecular dynamics (MD) and constant pH MD (CpHMD) simulations combined with umbrella sampling, transition path sampling, and Markov state models. Starting from the known crystal structures of HCA II and the monomeric catalytic domain of HCA IX (labeled as HCA IX-c), we have generated classical MD and CpHMD trajectories (of length 1 μs each). In all cases, the overall stability, RMSD, and secondary structure segments of the two isozymes are found to be quite similar. Functionally important dynamics of these two enzymes have been probed in terms of active site hydration, coordination of the Zn(II) ion to a transient excess water, and the formation of putative proton transfer paths. The most important difference between the two isozymes is observed for the side-chain fluctuations of His-64 that is expected to shuttle an excess proton out of the active site as a part of the rate-determining intramolecular proton transfer reaction. The relative stability of the stable inward and outward conformations of the His-64 side-chain and the underlying free energy surfaces are found to depend strongly on the isozyme. In each case, a lower free energy barrier is detected between predominantly inward conformations from predominantly outward ones when simulated under constant pH conditions. The kinetic rate constants of interconversion between different free energy basins are found to span 10⁷-10⁸ s^-1 with faster conformational transitions predicted at constant pH condition. The estimated rate constants and free energies are expected to validate if the fluctuation of the His-64 side-chain in HCA IX may have a significance similar to that known in the multistep catalytic cycle of HCA II.

Efficient proton shuttle makes SazCA an excellent CO2 hydration enzyme

The fastest member of the carbonic anhydrase family catalysing the reversible hydration of carbon dioxide to bicarbonate ions has been recently reported to be SazCA. While thermostable, this enzyme shows exceptional activity at 353 K for the reaction. This study explores the molecular basis for the exceptional activity of SazCA, in contrast to SspCA, probed using molecular dynamics simulations. Our simulations, carried out at different temperatures, indicate the presence of efficient proton shuttle between the active zinc centre and His64 residue in the two enzymes. The proton accepting His64 residue was identified to have in and out conformations with the in conformations being supportive to proton acceptance. Our simulations show a large population of in conformations in SazCA making the enzyme exhibit an exceptional activity. The RMSF and H-bonds analysis confirmed the role of His2 and His207 in supporting the attainment of in conformations in SazCA resulting in exceptional activity.Communicated by Ramaswamy H. Sarma.

Non-Markovian rate theory on a multidimensional reaction surface: Complex interplay between enhanced configuration space and memory

A theory of barrier crossing rate on a multidimensional reaction energy surface is presented. The theory is a generalization of the earlier theoretical schemes to higher dimensions, with the inclusion of non-Markovian friction along both the reactive and the nonreactive coordinates. The theory additionally includes the bilinear coupling between the reactive and the nonreactive modes at the Hamiltonian level. Under suitable conditions, we recover the rate expressions of Langer and Hynes and establish a connection with the rate treatment of Pollak. Within the phenomenology of generalized Langevin equation description, our formulation provides an improvement over the existing ones because we explicitly include both the non-Markovian effects along the reaction coordinate and the bilinear coupling at the Hamiltonian level. At intermediate-to-large friction, an increase in dimensionality by itself tends to reduce the rate, while the inclusion of the memory effects increases the rate. The theory predicts an increase in rate when off-diagonal friction terms are included. We present a model calculation to study isomerization of a stilbene-like molecule using the prescription of Hochstrasser and co-workers on a two-dimensional reaction energy surface, employing Zwanzig–Bixon hydrodynamic theory of frequency-dependent friction. The calculated rate shows a departure from the predictions of Langer’s theory and also from the two-dimensional transition state theory.

Nonlinear Reaction Coordinate of an Enzyme Catalyzed Proton Transfer Reaction

We present an in-depth study on the theoretical calculation of an optimum reaction coordinate as a linear or nonlinear combination of important collective variables (CVs) sampled from an ensemble of reactive transition paths for an intramolecular proton transfer reaction catalyzed by the enzyme human carbonic anhydrase (HCA) II. The linear models are optimized by likelihood maximization for a given number of CVs. The nonlinear models are based on an artificial neural network with the same number of CVs and optimized by minimizing the root-mean-square error in comparison to a training set of committor estimators generated for the given transition. The nonlinear reaction coordinate thus obtained yields the free energy of activation and rate constant as 9.46 kcal mol^-1 and 1.25 × 10⁶ s^-1, respectively. These estimates are found to be in quantitative agreement with the known experimental results. We have also used an extended autoencoder model to show that a similar analysis can be carried out using a single CV only. The resultant free energies and kinetics of the reaction slightly overestimate the experimental data. The implications of these results are discussed using a detailed microkinetic scheme of the proton transfer reaction catalyzed by HCA II.

Reaction Coordinate and Thermodynamics of Base Flipping in RNA

Base flipping is a key biophysical event involved in recognition of various ligands by ribonucleic acid (RNA) molecules. However, the mechanism of base flipping in RNA remains poorly understood, in part due to the lack of atomistic details on complex rearrangements in neighboring bases. In this work, we applied transition path sampling (TPS) methods to study base flipping in a double-stranded RNA (dsRNA) molecule that is known to interact with RNA-editing enzymes through this mechanism. We obtained an ensemble of 1000 transition trajectories to describe the base-flipping process. We used the likelihood maximization method to determine the refined reaction coordinate (RC) consisting of two collective variables (CVs), a distance and a dihedral angle between nucleotides that form stacking interactions with the flipping base. The free energy profile projected along the refined RC revealed three minima, two corresponding to the initial and final states and one for a metastable state. We suggest that the metastable state likely represents a wobbled conformation of nucleobases observed in NMR studies that is often characterized as the flipped state. The analyses of reactive trajectories further revealed that the base flipping is coupled to a global conformational change in a stem-loop of dsRNA.

Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.

Protein Flexibility and Stiffness Enable Efficient Enzymatic Catalysis

The enormous rate accelerations observed for many enzyme catalysts are due to strong stabilizing interactions between the protein and reaction transition state. The defining property of these catalysts is their specificity for binding the transition state with a much higher affinity than substrate. Experimental results are presented which show that the phosphodianion-binding energy of phosphate monoester substrates is used to drive conversion of their protein catalysts from flexible and entropically rich ground states to stiff and catalytically active Michaelis complexes. These results are generalized to other enzyme-catalyzed reactions. The existence of many enzymes in flexible, entropically rich, and inactive ground states provides a mechanism for utilization of ligand-binding energy to mold these catalysts into stiff and active forms. This reduces the substrate-binding energy expressed at the Michaelis complex, while enabling the full and specific expression of large transition-state binding energies. Evidence is presented that the complexity of enzyme conformational changes increases with increases in the enzymatic rate acceleration. The requirement that a large fraction of the total substrate-binding energy be utilized to drive conformational changes of floppy enzymes is proposed to favor the selection and evolution of protein folds with multiple flexible unstructured loops, such as the TIM-barrel fold. The effect of protein motions on the kinetic parameters for enzymes that undergo ligand-driven conformational changes is considered. The results of computational studies to model the complex ligand-driven conformational change in catalysis by triosephosphate isomerase are presented.

Perspective: Identification of collective variables and metastable states of protein dynamics

The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {x _i } = x that in some sense describe the essential dynamics of the system. Considering the distribution P( x ) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P( x ), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG( x ) = -k _B T ln P( x ), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.

In Silico Studies of Small Molecule Interactions with Enzymes Reveal Aspects of Catalytic Function

Small molecules, such as solvent, substrate, and cofactor molecules, are key players in enzyme catalysis. Computational methods are powerful tools for exploring the dynamics and thermodynamics of these small molecules as they participate in or contribute to enzymatic processes. In-depth knowledge of how small molecule interactions and dynamics influence protein conformational dynamics and function is critical for progress in the field of enzyme catalysis. Although numerous computational studies have focused on enzyme-substrate complexes to gain insight into catalytic mechanisms, transition states and reaction rates, the dynamics of solvents, substrates, and cofactors are generally less well studied. Also, solvent dynamics within the biomolecular solvation layer play an important part in enzyme catalysis, but a full understanding of its role is hampered by its complexity. Moreover, passive substrate transport has been identified in certain enzymes, and the underlying principles of molecular recognition are an area of active investigation. Enzymes are highly dynamic entities that undergo different conformational changes, which range from side chain rearrangement of a residue to larger-scale conformational dynamics involving domains. These events may happen nearby or far away from the catalytic site, and may occur on different time scales, yet many are related to biological and catalytic function. Computational studies, primarily molecular dynamics (MD) simulations, provide atomistic-level insight and site-specific information on small molecule interactions, and their role in conformational pre-reorganization and dynamics in enzyme catalysis. The review is focused on MD simulation studies of small molecule interactions and dynamics to characterize and comprehend protein dynamics and function in catalyzed reactions. Experimental and theoretical methods available to complement and expand insight from MD simulations are discussed briefly.

Coupling Protein Dynamics with Proton Transport in Human Carbonic Anhydrase II

The role of protein dynamics in enzyme catalysis is one of the most highly debated topics in enzymology. The main controversy centers around what may be defined as functionally significant conformational fluctuations and how, if at all, these fluctuations couple to enzyme catalyzed events. To shed light on this debate, the conformational dynamics along the transition path surmounting the highest free energy barrier have been herein investigated for the rate limiting proton transport event in human carbonic anhydrase (HCA) II. Special attention has been placed on whether the motion of an excess proton is correlated with fluctuations in the surrounding protein and solvent matrix, which may be rare on the picosecond and subpicosecond time scales of molecular motions. It is found that several active site residues, which do not directly participate in the proton transport event, have a significant impact on the dynamics of the excess proton. These secondary participants are shown to strongly influence the active site environment, resulting in the creation of water clusters that are conducive to fast, moderately slow, or slow proton transport events. The identification and characterization of these secondary participants illuminates the role of protein dynamics in the catalytic efficiency of HCA II.