Free Energy Barriers for Escape of Water Molecules from Protein Hydration Layer

Free energy barriers separating interfacial water molecules from the hydration layer at the surface of a protein to the bulk are obtained by using the umbrella sampling method of free energy calculation. We consider hydration layer of chicken villin head piece (HP-36) which has been studied extensively by molecular dynamics simulations. The free energy calculations reveal a strong sensitivity to the secondary structure. In particular, we find a region near the junction of first and second helix that contains a cluster of water molecules which are slow in motion, characterized by long residence times (of the order of 100 ps or more) and separated by a large free energy barrier from the bulk water. However, these ``slow'' water molecules constitute only about 5-10% of the total number of hydration layer water molecules. Nevertheless, they play an important role in stabilizing the protein conformation. Water molecules near the third helix (which is the important helix for biological function) are enthalpically least stable and exhibit the fastest dynamics. Interestingly, barrier height distributions of interfacial water are quite broad for water surrounding all the three helices (and the three coils), with the smallest barriers found for those near the helix-3. For the quasi-bound water molecules near the first and second helices, we use well-known Kramers' theory to estimate the residence time from the free energy surface, by estimating the friction along the reaction coordinate from the diffusion coefficient by using Einstein relation. The agreement found is satisfactory. We discuss the possible biological function of these slow, quasi-bound (but transient) water molecules on the surface.

Characterization of structural and free energy properties of promoters associated with Primary and Operon TSS in Helicobacter pylori genome and their orthologs

Promoter regions in the genomes of all domains of life show similar trends in several structural properties such as stability, bendability, curvature, etc. In current study we analysed the stability and bendability of various classes of promoter regions (based on the recent identification of different classes of transcription start sites) of Helicobacter pylori 26695 strain. It is found that primary TSS and operon-associated TSS promoters show significantly strong features in their promoter regions. DNA free-energy-based promoter prediction tool PromPredict was used to annotate promoters of different classes, and very high recall values (similar to 80%) are obtained for primary TSS. Orthologous genes from other strains of H. pylori show conservation of structural properties in promoter regions as well as coding regions. PromPredict annotates promoters of orthologous genes with very high recall and precision.

Free energy barriers for homogeneous crystal nucleation in a eutectic system of binary hard spheres

In this study, the free energy barriers for homogeneous crystal nucleation in a system that exhibits a eutectic point are computed using Monte Carlo simulations. The system studied is a binary hard sphere mixture with a diameter ratio of 0.85 between the smaller and larger hard spheres. The simulations of crystal nucleation are performed for the entire range of fluid compositions. The free energy barrier is found to be the highest near the eutectic point and is nearly five times that for the pure fluid, which slows down the nucleation rate by a factor of 10(-31). These free energy barriers are some of highest ever computed using simulations. For most of the conditions studied, the composition of the critical nucleus corresponds to either one of the two thermodynamically stable solid phases. However, near the eutectic point, the nucleation barrier is lowest for the formation of the metastable random hexagonal closed packed (rhcp) solid phase with composition lying in the two-phase region of the phase diagram. The fluid to solid phase transition is hypothesized to proceed via formation of a metastable rhcp phase followed by a phase separation into respective stable fcc solid phases.

Communication: Benzene dimer-The free energy landscape

Establishing the relative orientation of the two benzene molecules in the dimer has remained an enigmatic challenge. Consensus has narrowed the choice of structures to either a T-shape, that may be tilted, or a parallel displaced arrangement, but the relatively small energy differences makes identifying the global minimum difficult. Here we report an ab initio Car-Parrinello Molecular Dynamics based metadynamics computation of the free-energy landscape of the benzene dimer. Our calculations show that although competing structures may be isoenergetic, free energy always favors a tilted T-shape geometry at all temperatures where the bound benzene dimer exist. (C) 2013 AIP Publishing LLC.

Gibbs free energy of formation of rhodium sulfides

Using a solid-state electrochemical technique, thermodynamic properties of three sulfide phases (RhS0.882, Rh3S4, Rh2S3) in the binary system (Rh + S) are measured as a function of temperature over the range from (925 to 1275) K. Single crystal CaF2 is used as the electrolyte. The auxiliary electrode consisting of (CaS + CaF2) is designed in such a way that the sulfur chemical potential converts into an equivalent fluorine potential at each electrode. The sulfur potentials at the measuring electrodes are established by the mixtures of (Rh + RhS0.882), (RhS0.882 + Rh3S4) and (Rh3S4 + Rh2S3) respectively. A gas mixture (H-2 + H2S + Ar) of known composition fixes the sulfur potential at the reference electrode. A novel cell design with physical separation of rhodium sulfides in the measuring electrode from CaS in the auxiliary electrode is used to prevent interaction between the two sulfide phases. They equilibrate only via the gas phase in a hermetically sealed reference enclosure. Standard Gibbs energy changes for the following reactions are calculated from the electromotive force of three cells: 2.2667Rh (s) + S-2 (g) -> 2.2667RhS(0.882) (s), Delta(r)G degrees +/- 2330/(J . mol(-1)) = -288690 + 146.18 (T/K), 4.44RhS(0.882) (s) + S-2 (g) -> 1.48Rh(3)S(4) (s), Delta(r)G degrees +/- 2245/(J . mol(-1)) = -245596 + 164.31 (T/K), 4Rh(3)S(4) (s) + S-2 (g) -> 6Rh(2)S(3) (s), Delta(r)G degrees +/- 2490/(J . mol(-1)) = -230957 + 160: 03 (T/K). Standard entropy and enthalpy of formation of rhodium sulfides from elements in their normal standard states at T = 298.15 K are evaluated. (C) 2013 Elsevier Ltd. All rights reserved.

Propensity to Form Amyloid Fibrils Is Encoded as Excitations in the Free Energy Landscape of Monomeric Proteins

Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation-prone (N*) states, which are rarely populated under force free native conditions but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration (C]), mechanical force (f), and temperature exhibit an apparent two-state behavior, without revealing the presence of the elusive N* states. Interestingly, the phase boundaries separating the folded and unfolded states at all C] and f fall on a master curve, which can be quantitatively described using an analogy to superconductors in a magnetic field. The free energy profiles as a function of the molecular extension (R), which are accessible in pulling experiments, (R), reveal the presence of a native-like N* with a disordered solvent-exposed amino-terminal beta-strand. The structure of the N* state is identical with that found in Fyn SH3 by NMR dispersion experiments. We show that the timescale for fibril formation can be estimated from the population of the N* state, determined by the free energy gap separating the native structure and the N* state, a finding that can be used to assess fibril forming tendencies of proteins. The structures of the N* state are used to show that oligomer formation and likely route to fibrils occur by a domain-swap mechanism in SH3 domain. (C) 2014 Elsevier Ltd. All rights reserved.

Multidimensional free energy surface of unfolding of HP-36: Microscopic origin of ruggedness

The protein folding funnel paradigm suggests that folding and unfolding proceed as directed diffusion in a multidimensional free energy surface where a multitude of pathways can be traversed during the protein's sojourn from initial to final state. However, finding even a single pathway, with the detail chronicling of intermediates, is an arduous task. In this work we explore the free energy surface of unfolding pathway through umbrella sampling, for a small globular a-helical protein chicken-villin headpiece (HP-36) when the melting of secondary structures is induced by adding DMSO in aqueous solution. We find that the unfolding proceeds through the initial separation or melting of aggregated hydrophobic core that comprises of three phenylalanine residues (Phe7, Phe11, and Phe18). This separation is accompanied by simultaneous melting of the second helix. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hydrophobic grooves to stabilize the intermediate states. We identify the configuration of the intermediates and correlate the intermediates with those obtained in our previous works. We also give an estimate of the barriers for different transition states and observe the softening of the barriers with increasing DMSO concentration. We show that higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of a solvent modified, less rugged pathway. The prime outcome of this work is the demonstration that mixed solvents can profoundly transform the nature of the energy landscape and induce unfolding via a modified route. A successful application of Kramer's rate equation correlating the free energy simulation results shows faster rate of unfolding with increasing DMSO concentration. This work perhaps presents the first systematic theoretical study of the effect of a chemical denaturant on the microscopic free energy surface and rates of unfolding of HP-36. (C) 2014 AIP Publishing LLC.

Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.

Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution.

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

Free energy surface reconstruction from umbrella samples using Gaussian process regression

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.

Free energy surface reconstruction from umbrella samples using Gaussian process regression II: Multiple collective variables

We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive allows the concurrent use of histograms and free energy gradients and can easily be extended to include further data. In Part I we review the necessary theory and test the method for one collective variable. We demonstrate improved performance with respect to the weighted histogram analysis method and obtain meaningful error bars without any significant additional computation. In Part II we consider the case of multiple collective variables and compare to a reconstruction using least squares fitting of radial basis functions. We find substantial improvements in the regimes of spatially sparse data or short sampling trajectories. A software implementation is made available on www.libatoms.org.