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.

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.

Estimating Photosynthesis and Concurrent Export Rates in C3 and C4 Species at Ambient and Elevated CO21 2

The ability of 21 C3 and C4 monocot and dicot species to rapidly export newly fixed C in the light at both ambient and enriched CO2 levels was compared. Photosynthesis and concurrent export rates were estimated during isotopic equilibrium of the transport sugars using a steady-state 14CO2-labeling procedure. At ambient CO2 photosynthesis and export rates for C3 species were 5 to 15 and 1 to 10 μmol C m−2 s−1, respectively, and 20 to 30 and 15 to 22 μmol C m−2 s−1, respectively, for C4 species. A linear regression plot of export on photosynthesis rate of all species had a correlation coefficient of 0.87. When concurrent export was expressed as a percentage of photosynthesis, several C3 dicots that produced transport sugars other than Suc had high efflux rates relative to photosynthesis, comparable to those of C4 species. At high CO2 photosynthetic and export rates were only slightly altered in C4 species, and photosynthesis increased but export rates did not in all C3 species. The C3 species that had high efflux rates relative to photosynthesis at ambient CO2 exported at rates comparable to those of C4 species on both an absolute basis and as a percentage of photosynthesis. At ambient CO2 there were strong linear relationships between photosynthesis, sugar synthesis, and concurrent export. However, at high CO2 the relationships between photosynthesis and export rate and between sugar synthesis and export rate were not as strong because sugars and starch were accumulated.

Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

Elucidating the mechanism of folding of polynucleotides depends on accurate estimates of free energy surfaces and a quantitative description of the kinetics of structure formation. Here, the kinetics of hairpin formation in single-stranded DNA are measured after a laser temperature jump. The kinetics are modeled as configurational diffusion on a free energy surface obtained from a statistical mechanical description of equilibrium melting profiles. The effective diffusion coefficient is found to be strongly temperature-dependent in the nucleation step as a result of formation of misfolded loops that do not lead to subsequent zipping. This simple system exhibits many of the features predicted from theoretical studies of protein folding, including a funnel-like energy surface with many folding pathways, trapping in misfolded conformations, and non-Arrhenius folding rates.

Temperature dependence of the isotope chemistry of the heavy elements.

The temperature coefficient of equilibrium isotope fractionation in the heavy elements is shown to be larger at high temperatures than that expected from the well-studied vibrational isotope effects. The difference in the isotopic behavior of the heavy elements as compared with the light elements is due to the large nuclear isotope field shifts in the heavy elements. The field shifts introduce new mechanisms for maxima, minima, crossovers, and large mass-independent isotope effects in the isotope chemistry of the heavy elements. The generalizations are illustrated by the temperature dependence of the isotopic fractionation in the redox reaction between U(VI) and U(IV) ions.

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.

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)].

Mathematical modeling of drying process of unripe banana slices

Unripe banana flour (UBF) production employs bananas not submitted to maturation process, is an interesting alternative to minimize the fruit loss reduction related to inappropriate handling or fast ripening. The UBF is considered as a functional ingredient improving glycemic and plasma insulin levels in blood, have also shown efficacy on the control of satiety, insulin resistance. The aim of this work was to study the drying process of unripe banana slabs (Musa cavendishii, Nanicão) developing a transient drying model through mathematical modeling with simultaneous moisture and heat transfer. The raw material characterization was performed and afterwards the drying process was conducted at 40 ºC, 50 ºC e 60 ºC, the product temperature was recorded using thermocouples, the air velocity inside the chamber was 4 m·s-1. With the experimental data was possible to validate the diffusion model based on the Fick\'s second law and Fourier. For this purpose, the sorption isotherms were measured and fitted to the GAB model estimating the equilibrium moisture content (Xe), 1.76 [g H2O/100g d.b.] at 60 ºC and 10 % of relative humidity (RH), the thermophysical properties (k, Cp, ?) were also measured to be used in the model. Five cases were contemplated: i) Constant thermophysical properties; ii) Variable properties; iii) Mass (hm), heat transfer (h) coefficient and effective diffusivity (De) estimation 134 W·m-2·K-1, 4.91x10-5 m-2·s-1 and 3.278?10-10 m·s-2 at 60 ºC, respectively; iv) Variable De, it presented a third order polynomial behavior as function of moisture content; v) The shrinkage had an effect on the mathematical model, especially in the 3 first hours of process, the thickness experienced a contraction of about (30.34 ± 1.29) % out of the initial thickness, finding two decreasing drying rate periods (DDR I and DDR II), 3.28x10-10 m·s-2 and 1.77x10-10 m·s-2, respectively. COMSOL Multiphysics simulations were possible to perform through the heat and mass transfer coefficient estimated by the mathematical modeling.

Estudo de equilíbrio e cinética da biossorção de cobre (II) por Rhizopus Microsporus.

A poluição relacionada a metais pesados tem recebido uma atenção especial devido a sua alta toxicidade, não biodegradabilidade e tendência de acumular-se na cadeia alimentar. Apesar disso, metais pesados também são considerados recursos valiosos, portanto a sua remoção em conjunto com a sua recuperação torna-se ainda mais importante. Este caso aplica-se aos rejeitos de mineração de cobre, os quais oferecem a possibilidade de recuperação do metal e de sua contenção de maneira segura do meio ambiente. Tais rejeitos se caracterizam por ocuparem enormes áreas inundadas e abrigarem soluções diluídas de cobre (II), porém, muitas vezes, acima dos limites seguros. Diversos processos tradicionais de tratamento mostram-se disponíveis para remover o cobre de tais soluções, no entanto, em certas aplicações eles podem ser ineficientes ou muito onerosos. Nesse contexto, a biossorção é uma alternativa interessante. Nesse processo, certos microrganismos, como fungos, bactérias e algas, ligam-se passivamente ao cobre na forma íons ou outras moléculas em soluções. No presente trabalho foi avaliado o potencial de biossorção de íons cobre (II) pela biomassa do fungo Rhizopus microsporus, coletado e isolado da área de rejeitos da Mina do Sossego, na região norte do Brasil. Isotermas de biossorção foram determinadas experimentalmente em bateladas sob temperatura de 25°C, agitação de 150 rpm, concentração de biomassa de 2,0 a 2,5 g/L e tempo de contato mínimo de 4 horas. O pH mostrou ser um fator importante no equilíbrio da biossorção, sendo o valor máximo da capacidade de biossorção de 33,12 mg de cobre / g biomassa encontrado em pH 6. Valores sucessivamente menores são encontrados pela acidificação da solução, sendo o pH 1 considerado adequado para o processo de dessorção, correspondendo a uma capacidade de biossorção de 1,95 mg/g. Modelos de adsorção de Langmuir e de Freundlich ajustaram-se adequadamente às isotermas tanto com pH controlado quanto não controlado. Foi constatado que a troca iônica é um dos mecanismos envolvidos na biossorção do cobre com Rhizopus microsporus. Tanto o modelo de pseudo-primeira ordem quanto o de pseudo-segunda ordem ajustaram-se aos dados cinéticos da biossorção, sendo que o equilíbrio ocorre em aproximadamente 4 horas. A biomassa conservou a capacidade de biossorção ao operar repetidamente em três ciclos de sorção-dessorção. A biomassa viável e a morta não apresentaram diferença estatisticamente significativa na capacidade de biossorção.

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.