Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Electrostatic Contributions to the Thermodynamics of Ribonuclease P Protein Folding

Electrostatic interactions are of fundamental importance in determining the structure and stability of macromolecules. For example, charge-charge interactions modulate the folding and binding of proteins and influence protein solubility. Electrostatic interactions are highly variable and can be both favorable and unfavorable. The ability to quantify these interactions is challenging but vital to understanding the detailed balance and major roles that they have in different proteins and biological processes. Measuring pKa values of ionizable groups provides a sensitive method for experimentally probing the electrostatic properties of a protein.

pKa values report the free energy of site-specific proton binding and provide a direct means of studying protein folding and pH-dependent stability. Using a combination of NMR, circular dichroism, and fluorescence spectroscopy along with singular value decomposition, we investigated the contributions of electrostatic interactions to the thermodynamic stability and folding of the protein subunit of Bacillus subtilis ribonuclease P, P protein. Taken together, the results suggest that unfavorable electrostatics alone do not account for the fact that P protein is intrinsically unfolded in the absence of ligand because the pKa differences observed between the folded and unfolded state are small. Presumably, multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

Constructal dendritic configuration for the radiation heating of a solid stream

Here we show that the configuration of a slender enclosure can be optimized such that the radiation heating of a stream of solid is performed with minimal fuel consumption at the global level. The solid moves longitudinally at constant rate through the enclosure. The enclosure is heated by gas burners distributed arbitrarily, in a manner that is to be determined. The total contact area for heat transfer between the hot enclosure and the cold solid is fixed. We find that minimal global fuel consumption is achieved when the longitudinal distribution of heaters is nonuniform, with more heaters near the exit than the entrance. The reduction in fuel consumption relative to when the heaters are distributed uniformly is of order 10%. Tapering the plan view (the floor) of the heating area yields an additional reduction in overall fuel consumption. The best shape is when the floor area is a slender triangle on which the cold solid enters by crossing the base. These architectural features recommend the proposal to organize the flow of the solid as a dendritic design, which enters as several branches, and exits as a single hot stream of prescribed temperature. The thermodynamics of heating is presented in modern terms in the Sec. (exergy destruction, entropy generation). The contribution is that to optimize "thermodynamically" is the same as reducing the consumption of fuel. © 2010 American Institute of Physics.

Osmolyte-induced folding of an intrinsically disordered protein: folding mechanism in the absence of ligand.

Understanding the interconversion between thermodynamically distinguishable states present in a protein folding pathway provides not only the kinetics and energetics of protein folding but also insights into the functional roles of these states in biological systems. The protein component of the bacterial RNase P holoenzyme from Bacillus subtilis (P protein) was previously shown to be unfolded in the absence of its cognate RNA or other anionic ligands. P protein was used in this study as a model system to explore general features of intrinsically disordered protein (IDP) folding mechanisms. The use of trimethylamine N-oxide (TMAO), an osmolyte that stabilizes the unliganded folded form of the protein, enabled us to study the folding process of P protein in the absence of ligand. Transient stopped-flow kinetic traces at various final TMAO concentrations exhibited multiphasic kinetics. Equilibrium "cotitration" experiments were performed using both TMAO and urea during the titration to produce a urea-TMAO titration surface of P protein. Both kinetic and equilibrium studies show evidence of a previously undetected intermediate state in the P protein folding process. The intermediate state is significantly populated, and the folding rate constants are relatively slow compared to those of intrinsically folded proteins similar in size and topology. The experiments and analysis described serve as a useful example for mechanistic folding studies of other IDPs.

Thermodynamic analysis of ligand-induced changes in protein thermal unfolding applied to high-throughput determination of ligand affinities with extrinsic fluorescent dyes.

The quantification of protein-ligand interactions is essential for systems biology, drug discovery, and bioengineering. Ligand-induced changes in protein thermal stability provide a general, quantifiable signature of binding and may be monitored with dyes such as Sypro Orange (SO), which increase their fluorescence emission intensities upon interaction with the unfolded protein. This method is an experimentally straightforward, economical, and high-throughput approach for observing thermal melts using commonly available real-time polymerase chain reaction instrumentation. However, quantitative analysis requires careful consideration of the dye-mediated reporting mechanism and the underlying thermodynamic model. We determine affinity constants by analysis of ligand-mediated shifts in melting-temperature midpoint values. Ligand affinity is determined in a ligand titration series from shifts in free energies of stability at a common reference temperature. Thermodynamic parameters are obtained by fitting the inverse first derivative of the experimental signal reporting on thermal denaturation with equations that incorporate linear or nonlinear baseline models. We apply these methods to fit protein melts monitored with SO that exhibit prominent nonlinear post-transition baselines. SO can perturb the equilibria on which it is reporting. We analyze cases in which the ligand binds to both the native and denatured state or to the native state only and cases in which protein:ligand stoichiometry needs to treated explicitly.

Thermodynamic analysis of a molecular chaperone binding to unfolded protein substrates.

Molecular chaperones are a highly diverse group of proteins that recognize and bind unfolded proteins to facilitate protein folding and prevent nonspecific protein aggregation. The mechanisms by which chaperones bind their protein substrates have been studied for decades. However, there are few reports about the affinity of molecular chaperones for their unfolded protein substrates. Thus, little is known about the relative binding affinities of different chaperones and about the relative binding affinities of chaperones for different unfolded protein substrates. Here we describe the application of SUPREX (stability of unpurified proteins from rates of H-D exchange), an H-D exchange and MALDI-based technique, in studying the binding interaction between the molecular chaperone Hsp33 and four different unfolded protein substrates, including citrate synthase, lactate dehydrogenase, malate dehydrogenase, and aldolase. The results of our studies suggest that the cooperativity of the Hsp33 folding-unfolding reaction increases upon binding with denatured protein substrates. This is consistent with the burial of significant hydrophobic surface area in Hsp33 when it interacts with its substrate proteins. The SUPREX-derived K(d) values for Hsp33 complexes with four different substrates were all found to be within the range of 3-300 nM.

Elucidating solvent contributions to solution reactions with ab initio QM/MM methods.

Computer simulations of reaction processes in solution in general rely on the definition of a reaction coordinate and the determination of the thermodynamic changes of the system along the reaction coordinate. The reaction coordinate often is constituted of characteristic geometrical properties of the reactive solute species, while the contributions of solvent molecules are implicitly included in the thermodynamics of the solute degrees of freedoms. However, solvent dynamics can provide the driving force for the reaction process, and in such cases explicit description of the solvent contribution in the free energy of the reaction process becomes necessary. We report here a method that can be used to analyze the solvent contributions to the reaction activation free energies from the combined QM/MM minimum free-energy path simulations. The method was applied to the self-exchange S(N)2 reaction of CH(3)Cl + Cl(-), showing that the importance of solvent-solute interactions to the reaction process. The results were further discussed in the context of coupling between solvent and solute molecules in reaction processes.

Viscous state effect on the activity of Fe nanocatalysts.

Many applications of nanotubes and nanowires require controlled bottom-up engineering of these nanostructures. In catalytic chemical vapor deposition, the thermo-kinetic state of the nanocatalysts near the melting point is one of the factors ruling the morphology of the grown structures. We present theoretical and experimental evidence of a viscous state for nanoparticles near their melting point. The state exists over a temperature range scaling inversely with the catalyst size, resulting in enhanced self-diffusion and fluidity across the solid-liquid transformation. The overall effect of this phenomenon on the growth of nanotubes is that, for a given temperature, smaller nanoparticles have a larger reaction rate than larger catalysts.

Water exchange rates of water-soluble manganese(III) porphyrins of therapeutical potential.

The activation parameters and the rate constants of the water-exchange reactions of Mn(III)TE-2-PyP(5+) (meso-tetrakis(N-ethylpyridinium-2-yl)porphyrin) as cationic, Mn(III)TnHex-2-PyP(5+) (meso-tetrakis(N-n-hexylpyridinium-2-yl)porphyrin) as sterically shielded cationic, and Mn(III)TSPP(3-) (meso-tetrakis(4-sulfonatophenyl)porphyrin) as anionic manganese(iii) porphyrins were determined from the temperature dependence of (17)O NMR relaxation rates. The rate constants at 298 K were obtained as 4.12 x 10(6) s(-1), 5.73 x 10(6) s(-1), and 2.74 x 10(7) s(-1), respectively. On the basis of the determined entropies of activation, an interchange-dissociative mechanism (I(d)) was proposed for the cationic complexes (DeltaS(double dagger) = approximately 0 J mol(-1) K(-1)) whereas a limiting dissociative mechanism (D) was proposed for Mn(III)TSPP(3-) complex (DeltaS(double dagger) = +79 J mol(-1) K(-1)). The obtained water exchange rate of Mn(III)TSPP(3-) corresponded well to the previously assumed value used by Koenig et al. (S. H. Koenig, R. D. Brown and M. Spiller, Magn. Reson. Med., 1987, 4, 52-260) to simulate the (1)H NMRD curves, therefore the measured value supports the theory developed for explaining the anomalous relaxivity of Mn(III)TSPP(3-) complex. A magnitude of the obtained water-exchange rate constants further confirms the suggested inner sphere electron transfer mechanism for the reactions of the two positively charged Mn(iii) porphyrins with the various biologically important oxygen and nitrogen reactive species. Due to the high biological and clinical relevance of the reactions that occur at the metal site of the studied Mn(iii) porphyrins, the determination of water exchange rates advanced our insight into their efficacy and mechanism of action, and in turn should impact their further development for both diagnostic (imaging) and therapeutic purposes.

Acid-base and electrochemical properties of manganese meso(ortho- and meta-N-ethylpyridyl)porphyrins: potentiometric, spectrophotometric and spectroelectrochemical study of protolytic and redox equilibria.

The difference in electrostatics and reduction potentials between manganese ortho-tetrakis(N-ethylpyridinium-2-yl)porphyrin (MnTE-2-PyP) and manganese meta-tetrakis(N-ethylpyridinium-3-yl)porphyrin (MnTE-3-PyP) is a challenging topic, particularly because of the high likelihood for their clinical development. Hence, a detailed study of the protolytic and electrochemical speciation of Mn(II-IV)TE-2-PyP and Mn(II-IV)TE-3-PyP in a broad pH range has been performed using the combined spectrophotometric and potentiometric methods. The results reveal that in aqueous solutions within the pH range ∼2-13 the following species exist: (H(2)O)Mn(II)TE-m-PyP(4+), (HO)Mn(II)TE-m-PyP(3+), (H(2)O)(2)Mn(III)TE-m-PyP(5+), (HO)(H(2)O)Mn(III)TE-m-PyP(4+), (O)(H(2)O)Mn(III)TE-m-PyP(3+), (O)(H(2)O)Mn(IV)TE-m-PyP(4+) and (O)(HO)Mn(IV)TE-m-PyP(3+) (m = 2, 3). All the protolytic equilibrium constants that include the accessible species as well as the thermodynamic parameters for each particular protolytic equilibrium have been determined. The corresponding formal reduction potentials related to the reduction of the above species and the thermodynamic parameters describing the accessible reduction couples were calculated as well.

Radium and barium removal through blending hydraulic fracturing fluids with acid mine drainage.

Wastewaters generated during hydraulic fracturing of the Marcellus Shale typically contain high concentrations of salts, naturally occurring radioactive material (NORM), and metals, such as barium, that pose environmental and public health risks upon inadequate treatment and disposal. In addition, fresh water scarcity in dry regions or during periods of drought could limit shale gas development. This paper explores the possibility of using alternative water sources and their impact on NORM levels through blending acid mine drainage (AMD) effluent with recycled hydraulic fracturing flowback fluids (HFFFs). We conducted a series of laboratory experiments in which the chemistry and NORM of different mix proportions of AMD and HFFF were examined after reacting for 48 h. The experimental data combined with geochemical modeling and X-ray diffraction analysis suggest that several ions, including sulfate, iron, barium, strontium, and a large portion of radium (60-100%), precipitated into newly formed solids composed mainly of Sr barite within the first ∼ 10 h of mixing. The results imply that blending AMD and HFFF could be an effective management practice for both remediation of the high NORM in the Marcellus HFFF wastewater and beneficial utilization of AMD that is currently contaminating waterways in northeastern U.S.A.

Thermodynamic and dynamic contributions to future changes in regional precipitation variance: focus on the Southeastern United States

© 2014, Springer-Verlag Berlin Heidelberg.The frequency and severity of extreme events are tightly associated with the variance of precipitation. As climate warms, the acceleration in hydrological cycle is likely to enhance the variance of precipitation across the globe. However, due to the lack of an effective analysis method, the mechanisms responsible for the changes of precipitation variance are poorly understood, especially on regional scales. Our study fills this gap by formulating a variance partition algorithm, which explicitly quantifies the contributions of atmospheric thermodynamics (specific humidity) and dynamics (wind) to the changes in regional-scale precipitation variance. Taking Southeastern (SE) United States (US) summer precipitation as an example, the algorithm is applied to the simulations of current and future climate by phase 5 of Coupled Model Intercomparison Project (CMIP5) models. The analysis suggests that compared to observations, most CMIP5 models (~60 %) tend to underestimate the summer precipitation variance over the SE US during the 1950–1999, primarily due to the errors in the modeled dynamic processes (i.e. large-scale circulation). Among the 18 CMIP5 models analyzed in this study, six of them reasonably simulate SE US summer precipitation variance in the twentieth century and the underlying physical processes; these models are thus applied for mechanistic study of future changes in SE US summer precipitation variance. In the future, the six models collectively project an intensification of SE US summer precipitation variance, resulting from the combined effects of atmospheric thermodynamics and dynamics. Between them, the latter plays a more important role. Specifically, thermodynamics results in more frequent and intensified wet summers, but does not contribute to the projected increase in the frequency and intensity of dry summers. In contrast, atmospheric dynamics explains the projected enhancement in both wet and dry summers, indicating its importance in understanding future climate change over the SE US. The results suggest that the intensified SE US summer precipitation variance is not a purely thermodynamic response to greenhouse gases forcing, and cannot be explained without the contribution of atmospheric dynamics. Our analysis provides important insights to understand the mechanisms of SE US summer precipitation variance change. The algorithm formulated in this study can be easily applied to other regions and seasons to systematically explore the mechanisms responsible for the changes in precipitation extremes in a warming climate.

Conformational kinetics reveals affinities of protein conformational states.

Most biological reactions rely on interplay between binding and changes in both macromolecular structure and dynamics. Practical understanding of this interplay requires detection of critical intermediates and determination of their binding and conformational characteristics. However, many of these species are only transiently present and they have often been overlooked in mechanistic studies of reactions that couple binding to conformational change. We monitored the kinetics of ligand-induced conformational changes in a small protein using six different ligands. We analyzed the kinetic data to simultaneously determine both binding affinities for the conformational states and the rate constants of conformational change. The approach we used is sufficiently robust to determine the affinities of three conformational states and detect even modest differences in the protein's affinities for relatively similar ligands. Ligand binding favors higher-affinity conformational states by increasing forward conformational rate constants and/or decreasing reverse conformational rate constants. The amounts by which forward rate constants increase and reverse rate constants decrease are proportional to the ratio of affinities of the conformational states. We also show that both the affinity ratio and another parameter, which quantifies the changes in conformational rate constants upon ligand binding, are strong determinants of the mechanism (conformational selection and/or induced fit) of molecular recognition. Our results highlight the utility of analyzing the kinetics of conformational changes to determine affinities that cannot be determined from equilibrium experiments. Most importantly, they demonstrate an inextricable link between conformational dynamics and the binding affinities of conformational states.

MRI-Guided Radiation Therapy: Investigating the Accuracy of Treatment Delivery

Purpose: To develop, evaluate and apply a novel high-resolution 3D remote dosimetry protocol for validation of MRI guided radiation therapy treatments (MRIdian® by ViewRay®). We demonstrate the first application of the protocol (including two small but required new correction terms) utilizing radiochromic 3D plastic PRESAGE® with optical-CT readout.

Methods: A detailed study of PRESAGE® dosimeters (2kg) was conducted to investigate the temporal and spatial stability of radiation induced optical density change (ΔOD) over 8 days. Temporal stability was investigated on 3 dosimeters irradiated with four equally-spaced square 6MV fields delivering doses between 10cGy and 300cGy. Doses were imaged (read-out) by optical-CT at multiple intervals. Spatial stability of ΔOD response was investigated on 3 other dosimeters irradiated uniformly with 15MV extended-SSD fields with doses of 15cGy, 30cGy and 60cGy. Temporal and spatial (radial) changes were investigated using CERR and MATLAB’s Curve Fitting Tool-box. A protocol was developed to extrapolate measured ΔOD readings at t=48hr (the typical shipment time in remote dosimetry) to time t=1hr.

Results: All dosimeters were observed to gradually darken with time (<5% per day). Consistent intra-batch sensitivity (0.0930±0.002 ΔOD/cm/Gy) and linearity (R2=0.9996) was observed at t=1hr. A small radial effect (<3%) was observed, attributed to curing thermodynamics during manufacture. The refined remote dosimetry protocol (including polynomial correction terms for temporal and spatial effects, CT and CR) was then applied to independent dosimeters irradiated with MR-IGRT treatments. Excellent line profile agreement and 3D-gamma results for 3%/3mm, 10% threshold were observed, with an average passing rate 96.5%± 3.43%.

Conclusion: A novel 3D remote dosimetry protocol is presented capable of validation of advanced radiation treatments (including MR-IGRT). The protocol uses 2kg radiochromic plastic dosimeters read-out by optical-CT within a week of treatment. The protocol requires small corrections for temporal and spatially-dependent behaviors observed between irradiation and readout.

Phonon anharmonicity and negative thermal expansion in SnSe

The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Including the anisotropic strain dependence of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.