Suman Chakrabarty

Exploration of the cytochrome c oxidase pathway puzzle and examination of the origin of elusive mutational effects

Gaining detailed understanding of the energetics of the proton-pumping process in cytochrome c oxidase (CcO) is a problem of great current interest. Despite promising mechanistic proposals, so far, a physically consistent model that would reproduce all the relevant barriers needed to create a working pump has not been presented. In addition, there are major problems in elucidating the origin of key mutational effects and in understanding the nature of the apparent pK(a) values associated with the pH dependencies of specific proton transfer (PT) reactions in CcO. This work takes a key step in resolving the above problems, by considering mutations, such as the Asn139Asp replacement, that blocks proton pumping without affecting PT to the catalytic site. We first introduce a formulation that makes it possible to relate the apparent pK(a) of Glu286 to different conformational states of this residue. We then use the new formulation along with the calculated pK(a) values of Glu286 at these different conformations to reproduce the experimentally observed apparent pK(a) of the residue. Next, we take the X-ray structures of the native and Asn139Asp mutant of the Paracoccus denitrificans CcO (N131D in this system) and reproduce for the first time the change in the primary PT pathways (and other key features) based on simulations that start with the observed structural changes. We also consider the competition between proton transport to the catalytic site and the pump site, as a function of the bulk pH, as well as the H/D isotope effect, and use this information to explore the relative height of the two barriers. The paper emphasizes the crucial role of energy-based considerations that include the PT process, and the delicate control of PT in CcO.

Quantifying the Mechanism of Phosphate Monoester Hydrolysis in Aqueous Solution by Evaluating the Relevant Ab Initio QM/MM Free-Energy Surfaces

Understanding the nature of the free-energy surfaces for phosphate hydrolysis is a prerequisite for understanding the corresponding key chemical reactions in biology. Here, the challenge has been to move to careful ab initio QM/MM (QM(ai)/MM) free-energy calculations, where obtaining converging results is very demanding and computationally expensive. This work describes such calculations, focusing on the free-energy surface for the hydrolysis of phosphate monoesters, paying special attention to the comparison between the one water (1W) and two water (2W) paths for the proton-transfer (PT) step. This issue has been explored before by energy minimization with implicit solvent models and by nonsystematic QM/MM energy minimization, as well as by nonsystematic free-energy mapping. However, no study has provided the needed reliable 2D (3D) surfaces that are necessary for reaching concrete conclusions. Here we report a systematic evaluation of the 2D (3D) free-energy maps for several relevant systems, comparing the results of QM(ai)/MM and QM(ai)/implicit solvent surfaces, and provide an advanced description of the relevant energetics. It is found that the 1W path for the hydrolysis of the methyl diphosphate (MDP) trianion is 6-9 kcal/mol higher than that the 2W path. This difference becomes slightly larger in the presence of the Mg(2+) ion because this ion reduces the pKa of the conjugated acid form of the phosphate oxygen that accepts the proton. Interestingly, the BLYP approach (which has been used extensively in some studies) gives a much smaller difference between the 1W and 2W activation barriers. At any rate, it is worth pointing out that the 2W transition state for the PT is not much higher that the common plateau that serves as the starting point of both the 1W and 2W PT paths. Thus, the calculated catalytic effects of proteins based on the 2W PT mechanistic model are not expected to be different from the catalytic effects predicted using the 1W PT mechanistic model, which was calibrated on the observed barrier in solution and in which the TS charge distribution was similar to the that of the plateau (as was done in all of our previous EVB studies).

Anomalous behavior of linear hydrocarbon chains in water-DMSO binary mixture at low DMSO concentration.

We find that at a mole fraction 0.05 of DMSO (x(DMSO) = 0.05) in aqueous solution, a linear hydrocarbon chain of intermediate length (n=30-40) adopts the most stable collapsed conformation. In pure water, the same chain exhibits an intermittent oscillation between the collapsed and the extended coiled conformations. Even when the mole fraction of DMSO in the bulk is 0.05, the concentration of the same in the first hydration layer around the hydrocarbon of chain length 30 (n=30) is as large as 17%. Formation of such hydrophobic environment around the hydrocarbon chain may be viewed as the reason for the collapsed conformation gaining additional stability. We find a second anomalous behavior to emerge near x(DMSO)=0.15, due to a chain-like aggregation of the methyl groups of DMSO in water that lowers the relative concentration of the DMSO molecules in the hydration layer. We further find that as the concentration of DMSO is gradually increased, it progressively attains the extended coiled structure as the stable conformation. Although Flory-Huggins theory (for binary mixture solvent) fails to predict the anomaly at x(DMSO)=0.05, it seems to capture the essence of the anomaly at 0.15.

Capturing the energetics of water insertion in biological systems: The water flooding approach

Consistent description of the effect of internal water in proteins has been a major challenge for both simulation and experimental studies. Describing this effect has been particularly important and elusive in cases of charges in protein interiors. Here, we present a new microscopic method that provides an efficient way for simulating the energetics of water insertion. Instead of performing explicit Monte Carlo (MC) moves on the insertion process, which generally involves an enormous number of rejected attempts, our method is based on generating trial configurations with excess amount of internal water, estimating the relevant free energy by the linear response approximation, and then using a postprocessing MC treatment to filter out a limited number of configurations from a large possible set. Our approach is validated on particularly challenging test cases including the pKa of the V66D mutation in Staphylococcal nuclease, Glu286 in cytochrome c oxidase (CcO) and the energetics of a protonated water molecule in the D channel of CcO. The new postprocessing method allows us to reproduce the relevant energetics of highly unstable charges in protein interiors using fully microscopic calculations and provides a substantial improvement over regular microscopic free energy estimates. This advance established the effectiveness of our water insertion strategy in challenging cases that have not been addressed successfully by other microscopic methods. Furthermore, our study provides a new exciting view on the crucial effect of water penetration in key biological systems as well as a new view on the nature of the dielectric in protein interiors. Proteins 2013.

Realistic simulation of the activation of voltage-gated ion channels

Understanding the detailed mechanism of the activation of voltage-gated ion channels has been a problem of great current interest. Reliable molecular simulations of voltage effects present a major challenge because meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties regarding the dielectric constant used and other key features. The current work has overcome some of the above challenges by using our recently developed coarse-grained (CG) model in simulating the activation of the Kv1.2 channel. The CG model has allowed us to explore problems that cannot be addressed at present by fully microscopic simulations, while providing insights on some features that are not usually considered in continuum models, including the distribution of the electrolytes between the membrane and the electrodes during the activation process and thus the nature of the gating current. Furthermore, the clear connection to microscopic descriptions combined with the power of CG modeling offers a powerful tool for exploring the energy balance between the protein conformational energy and the interaction with the external potential in voltage-activated channels. Our simulations have reproduced the observed experimental trend of the gating charge and, most significantly, the correct trend in the free energies, where the closed channel is more stable at negative potential and the open channel is more stable at positive potential. Moreover, we provide a unique view of the activation landscape and the time dependence of the activation process.

Coarse grained model for exploring voltage dependent ion channels.

The relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention is devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes plus the electrolytes and the protein ionized groups. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye-Huckel, and the Gouy-Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. To illustrate these features we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the close to open voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function.

Correlating Nitrile IR Frequencies to Local Electrostatics Quantifies Noncovalent Interactions of Peptides and Proteins

Noncovalent interactions, in particular the hydrogen bonds and nonspecific long-range electrostatic interactions are fundamental to biomolecular functions. A molecular understanding of the local electrostatic environment, consistently for both specific (hydrogen-bonding) and nonspecific electrostatic (local polarity) interactions, is essential for a detailed understanding of these processes. Vibrational Stark Effect (VSE) has proven to be an extremely useful method to measure the local electric field using infrared spectroscopy of carbonyl and nitrile based probes. The nitrile chemical group would be an ideal choice because of its absorption in an infrared spectral window transparent to biomolecules, ease of site-specific incorporation into proteins, and common occurrence as a substituent in various drug molecules. However, the inability of VSE to describe the dependence of IR frequency on electric field for hydrogen-bonded nitriles to date has severely limited nitriles utility to probe the noncovalent interactions. In this work, using infrared spectroscopy and atomistic molecular dynamics simulations, we have reported for the first time a linear correlation between nitrile frequencies and electric fields in a wide range of hydrogen-bonding environments that may bridge the existing gap between VSE and H-bonding interactions. We have demonstrated the robustness of this field-frequency correlation for both aromatic nitriles and sulfur-based nitriles in a wide range of molecules of varying size and compactness, including small molecules in complex solvation environments, an amino acid, disordered peptides, and structured proteins. This correlation, when coupled to VSE, can be used to quantify noncovalent interactions, specific or nonspecific, in a consistent manner.

Self-Organization of n-Alkane Chains in Water: Length Dependent Crossover from Helix and Toroid to Molten Globule

We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n<or=20) and spherical for very long ones (n=100), we find the emergence of ordered helical structures at intermediate lengths (n approximately 40). We find different types of disordered helices and toroid-like structures at n=60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n=30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.

Universal Power Law in the Orientational Relaxation in Thermotropic Liquid Crystals

We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.

Effect of Solvation on Electron Detachment and Excitation Energies of a Green Fluorescent Protein Chromophore Variant

Hybrid quantum mechanics/molecular mechanics (QM/MM) is applied to the fluorinated green fluorescent protein (GFP) chromophore (DFHBDI) in its deprotonated form to understand the solvatochromic shifts in its vertical detachment energy (VDE) and vertical excitation energy (VEE). This variant of the GFP chromophore becomes fluorescent in an RNA environment and has a wide range of applications in biomedical and biochemical fields. From microsolvation studies, we benchmark (with respect to full QM) the accuracy of our QM/MM calculations with effective fragment potential (EFP) as the MM method of choice. We show that while the solvatochromic shift in the VEE is minimal (0.1 eV blue shift) and its polarization component is only 0.03 eV, the effect of the solvent on the VDE is quite large (3.85 eV). We also show by accurate calculations on the solvatochromic shift of the VDE that polarization accounts for ∼0.23 eV and therefore cannot be neglected. The effect of the counterions on the VDE of the deprotonated chromophore in solvation is studied in detail, and a charge-smearing scheme is suggested for charged chromophores.