An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

NMR investigation of ferricytochrome c unfolding: Detection of an equilibrium unfolding intermediate and residual structure in the denatured state

Horse ferricytochrome c (cyt c) undergoes exchange of one of its axial heme ligands (Met-80) for one or more non-native ligands under denaturing conditions. We have used 1H NMR spectroscopy to detect two conformations of paramagnetic cyt c with non-native heme ligation through a range of urea concentrations. One non-native form is an equilibrium unfolding intermediate observed under partially denaturing conditions and is attributed to replacement of Met-80 with one or more Lys side chains. The second non-native form, in which the native Met ligand is replaced by a His, is observed under strongly denaturing conditions. Thermodynamic analysis of these data indicates a relatively small ΔG (17 kJ/mol) for the transition from native to the Lys-ligated intermediate and a significantly larger ΔG (47 kJ/mol) for the transition from native to the His-ligated species. Although CD and fluorescence data indicate that the equilibrium unfolding of cyt c is a two-state process, these NMR results implicate an intermediate with His-Lys ligation.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: High-pressure and cosolute studies on recombinant human IFN-γ

The equilibrium dissociation of recombinant human IFN-γ was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was −209 ± 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 ± 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-γ in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were −41 ± 9 ml/mol of dimer and 3.5 ± 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values ≈4-fold larger for both transitions.

Phosphorylation by protein kinase C of serine-23 of the alpha-1 subunit of rat Na+,K(+)-ATPase affects its conformational equilibrium.

Phosphorylation of the alpha-1 subunit of rat Na+,K(+)-ATPase by protein kinase C has been shown previously to decrease the activity of the enzyme in vitro. We have now undertaken an investigation of the mechanism by which this inhibition occurs. Analysis of the phosphorylation of recombinant glutathione S-transferase fusion proteins containing putative cytoplasmic domains of the protein, site-directed mutagenesis, and two-dimensional peptide mapping indicated that protein kinase C phosphorylated the alpha-1 subunit of the rat Na+,K(+)-ATPase within the extreme NH2-terminal domain, on serine-23. The phosphorylation of this residue resulted in a shift in the equilibrium toward the E1 form, as measured by eosin fluorescence studies, and this was associated with a decrease in the apparent K+ affinity of the enzyme, as measured by ATPase activity assays. The rate of transition from E2 to E1 was apparently unaffected by phosphorylation by protein kinase C. These results, together with previous studies that examined the effects of tryptic digestion of Na+,K(+)-ATPase, suggest that the NH2-terminal domain of the alpha-1 subunit, including serine-23, is involved in regulating the activity of the enzyme.

Probing active galactic nuclei with H2O megamasers.

We describe the characteristics of the rapidly rotating molecular disk in the nucleus of the mildly active galaxy NGC4258. The morphology and kinematics of the disk are delineated by the point-like watervapor emission sources at 1.35-cm wavelength. High angular resolution [200 microas where as is arcsec, corresponding to 0.006 parsec (pc) at 6.4 million pc] and high spectral resolution (0.2 km.s-1 or nu/Deltanu = 1.4 x 10(6)) with the Very-Long-Baseline Array allow precise definition of the disk. The disk is very thin, but slightly warped, and is viewed nearly edge-on. The masers show that the disk is in nearly perfect Keplerian rotation within the observable range of radii of 0.13-0.26 pc. The approximately random deviations from the Keplerian rotation curve among the high-velocity masers are approximately 3.5 km.s-1 (rms). These deviations may be due to the masers lying off the midline by about +/-4 degrees or variations in the inclination of the disk by +/-4 degrees. Lack of systematic deviations indicates that the disk has a mass of <4 x 10(6) solar mass (M[symbol: see text]). The gravitational binding mass is 3.5 x 10(7) M[symbol: see text], which must lie within the inner radius of the disk and requires that the mass density be >4 x 10(9) M[symbol: see text].pc-3. If the central mass were in the form of a star cluster with a density distribution such as a Plummer model, then the central mass density would be 4 x 10(12) M[symbol: see text].pc-3. The lifetime of such a cluster would be short with respect to the age of the galaxy [Maoz, E. (1995) Astrophys. J. Lett. 447, L91-L94]. Therefore, the central mass may be a black hole. The disk as traced by the systemic velocity features is unresolved in the vertical direction, indicating that its scale height is <0.0003 pc (hence the ratio of thickness to radius, H/R, is <0.0025). For a disk in hydrostatic equilibrium the quadrature sum of the sound speed and Alfven velocity is <2.5 km.s-1, so that the temperature of the disk must be <1000 K and the toroidal magnetic field component must be <250 mG. If the molecular mass density in the disk is 10(10) cm-3, then the disk mass is approximately 10(4) M[symbol: see text], and the disk is marginally stable as defined by the Toomre stability parameter Q (Q = 6 at the inner edge and 1 at the outer edge). The inward drift velocity is predicted to be <0.007 km.s-1, for a viscosity parameter of 0.1, and the accretion rate is <7 x 10(-5) M[symbol: see text].yr-1. At this value the accretion would be sufficient to power the nuclear x-ray source of 4 x 10(40) ergs-1 (1 erg = 0.1 microJ). The volume of individual maser components may be as large as 10(46) cm3, based on the velocity gradients, which is sufficient to supply the observed luminosity. The pump power undoubtedly comes from the nucleus, perhaps in the form of x-rays. The warp may allow the pump radiation to penetrate the disk obliquely [Neufeld, D. A. & Maloney, P. R. (1995) Astrophys. J. Lett. 447, L17-L19]. A total of 15 H2O megamasers have been identified out of >250 galaxies searched. Galaxy NGC4258 may be the only case where conditions are optimal to reveal a well-defined nuclear disk. Future measurement of proper motions and accelerations for NGC4258 will yield an accurate distance and a more precise definition of the dynamics of the disk

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs’ free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p_(co) = 11.5727(10)k_(B)T/σ^(3)] and the interfacial free energy [γ_({100}) = 0.636(11)k_(B)T/σ^(2)].

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

Correlation of the liquid–liquid equilibrium data for specific ternary systems with one or two partially miscible binary subsystems

This paper presents the results of a liquid–liquid equilibrium data correlation for 11 ternary systems which have not been previously fitted using the NRTL model or, when they have, the results presented in the literature are inconsistent with the experimental behavior of the system. These ternary systems include mixtures with one or two partially miscible pairs. During the correlation process, new restrictions were imposed on the values for the NRTL binary parameters to ensure correct prediction of the total or partial miscibility for the binary pairs involved. In addition, topological concepts related to the Gibbs stability test have been applied in order to validate the results in the whole range of compositions.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.