Dynamic Equilibrium System Research Articles

The Cardiac Ca 2+-Sensitive Regulatory Switch, a System in Dynamic Equilibrium

The Ca 2+-sensitive regulatory switch of cardiac muscle is a paradigmatic example of protein assemblies that communicate ligand binding through allosteric change. The switch is a dimeric complex of troponin C (TnC), an allosteric sensor for Ca 2+, and troponin I (TnI), an allosteric reporter. Time-resolved equilibrium Förster resonance energy transfer (FRET) measurements suggest that the switch activates in two steps: a TnI-independent Ca 2+-priming step followed by TnI-dependent opening. To resolve the mechanistic role of TnI in activation we performed stopped-flow FRET measurements of activation after rapid addition of a lacking component (Ca 2+ or TnI) and deactivation after rapid chelation of Ca 2+. Time-resolved measurements, stopped-flow measurements, and Ca 2+-titration measurements were globally analyzed in terms of a new quantitative dynamic model of TnC-TnI allostery. The analysis provided a mesoscopic parameterization of distance changes, free energy changes, and transition rates among the accessible coarse-grained states of the system. The results reveal that 1), the Ca 2+-induced priming step, which precedes opening, is the rate-limiting step in activation; 2), closing is the rate-limiting step in de-activation; 3), TnI induces opening; 4), there is an incompletely deactivated population when regulatory Ca 2+ is not bound, which generates an accessory pathway of activation; and 5), there is incomplete activation by Ca 2+—when regulatory Ca 2+ is bound, a 3:2 mixture of dynamically interconverting open (active) and primed-closed (partially active) conformers is observed (15°C). Temperature-dependent stopped-flow FRET experiments provide a near complete thermokinetic parameterization of opening: the enthalpy change (Δ H = −33.4 kJ/mol), entropy change (Δ S = −0.110 kJ/mol/K), heat capacity change (Δ C p = −7.6 kJ/mol/K), the enthalpy of activation ( δ ‡ = 10.6 kJ/mol) and the effective barrier crossing attempt frequency ( ν adj = 1.8 × 10 4 s −1).

Design variable tolerance effects on the natural frequency variance of constrained multi-body systems in dynamic equilibrium

The design variable tolerance effects on the natural frequency variance of constrained multi-body systems in dynamic equilibrium are investigated in this study. Monte-Carlo simulation is often employed for such investigations, but it is known to have serious drawbacks. Excessive amount of computation time needs to be consumed since a large number of evaluations are usually required for the method. Furthermore, the solution accuracy cannot be always guaranteed in spite of the excessive amount of computation time. In order to overcome such drawbacks, a method employing eigenvalue sensitivity information is proposed to obtain the variance of natural frequency in this study. In order to verify the accuracy and the efficiency of the method, some numerical examples of multi-body systems in dynamic equilibrium are solved and the results are compared to those obtained by an analytical method and Monte-Carlo simulation.

The Persistence of Universal Halo Profiles

We have performed simple simulations which suggest that the phase-space structure of halos identified in cosmological calculations is invariant under the dynamics induced by sinking substructure satellites. This contention is confirmed using a two-component Fokker-Planck formulation, representing the dynamics of a smooth background and a system of massive clumps. It is shown that, to very high accuracy, when the clumps sink in under the action of dynamical friction, the background expands so as to leave the total distribution unchanged. This holds for the inner and intermediate regions of isotropic systems in dynamical equilibrium, and is valid for any mass spectrum of substructure, because the governing equation is linear in their mass-weighted phase-space distribution. If the clumps are considered solid, the process whereby background particles are driven out of low-energy states takes the form of an exponential instability, with a characteristic timescale on the order of the dynamical friction time, on which develops a low-energy cutoff in the phase-space distribution of these lighter particles and a constant-density core in their spatial distribution. This could correspond to a situation in which the clumps are made of dense baryonic material. We also considered the case when stripping is strong enough for a low-energy cutoff to develop in the clump distribution (as in the situation with dissipationless substructure). The results of this paper suggest that halo profiles similar to those found in dissipationless cosmological simulations are approximately invariant under the interaction induced by the presence of substructure, a necessary condition for the observed universality. In addition, the total profile, including baryons, should also be invariant, provided that the latter are initially in the form of dense clumps, whose distribution initially follows that of dark matter.

L’Homme, victime de son cerveau ?

Is the obesity pandemia resulting from an inadequate human physiology faced to a changing alimentary environment or is it the consequence of his own peculiarities leading him to build himself an unadapted environment, thus differing from animals like apes (monkeys)?We propose an enlarged conceptual organization of the regulation of food intake and body mass. It would imply four partners. The level of energy intake, metabolic energy utilisation, the level of fat stores and functional digestive ability. Each of these four players would be a controlled variable in relation to the three others and at the same time working towards their control in a system in dynamic equilibrium. They would be under the permanent control of a central integrator able to limit the variation of the center of gravity of the system in acceptable bounds relatively to an individual set point.A number of physiologic knowledges support this concept and we may insist on the role of visceral sensitivity and central integration. The refinement of the regulation of our integrity offering important adaptative mechanisms lead us to consider that human physiology is able to cope with usual changes of our alimentary environment.By exploring what coud differenciate humans from animals, particularly apes, the idea arises that humans could be victimized by his cognitive capabilities and more particularly by his communicative capabilities. Able to construct and to infer from incomplete knowledge he is capable to build up an unadapted environment driving him to destruction.Again, whatever their illusions human beeings cannot infrige their physiologic limits.

On the Characterization of Dynamic Supramolecular Systems: A General Mathematical Association Model for Linear Supramolecular Copolymers and Application on a Complex Two‐Component Hydrogen‐Bonding System

A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab, and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4n5m as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the DeltaH degrees and DeltaS degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters.

Pancreatic hydrolysis of bovine casein: Changes in the aggregate size and molecular weight distribution

The effect of pancreatic hydrolysis on the aggregate size and molecular weight distribution (MWD) of bovine casein was investigated by size exclusion chromatography (SEC), coupled with multiangle laser light scattering (MALLS) and dynamic light scattering (DLS). The concentrations of both casein aggregates and monomers decreased as the reaction proceeded and almost disappeared after a 10 min hydrolysis. The ratio of aggregates to monomers was maintained at 1:(2–2.5) during the initial 10 min hydrolysis, which shows that the caseins in the solution are in a dynamic equilibrium system, between aggregates and monomers. Upon limited hydrolysis, casein aggregates displayed a continuous growth in their sizes and molecular weights, together with a decrease in the intermolecular repulsion. This result was further supported by on-line DLS measurements, which showed the increase in the hydrodynamic radii and the decrease in light scattering intensities of casein hydrolysates. Moreover, the release kinetics of peptide fractions with different molecular weights were also followed. It was suggested that the increase in the hydrophobic attraction and the reduction in the protein repulsion might promote casein aggregation, during the limited pancreatic hydrolysis.

Solubility measurement of methyl anthranilate in supercritical carbon dioxide using dynamic and static equilibrium systems

AbstractThe solubility of methyl anthranilate in supercritical carbon dioxide was determined using dynamic and static equilibrium systems. Three temperatures (40, 60 and 80 °C) and a pressure range between 160 and 340 atm were applied for the dynamic solubility measurements. The flow rate was maintained at 0.5 mL min−1 in the dynamic solubility measurements, where the solute solubility was claimed to be independent of the flow‐rate factor. Two temperatures (40 and 60 °C) and the pressure range between 100 and 265 atm were used in the static equilibrium system. The crossover pressure region was observed between 220 and 240 atm in the static system, but was not seen in the dynamic system. The solubility of methyl anthranilate determined by the static system was consistently higher than the dynamic solubility measurement, indicating that the static technique provided more reliable solubility data for methyl anthranilate than the dynamic technique. The solubility data obtained with the static system were in good agreement with the predictive models based on the Chrastil equation and the Peng–Robinson equation of state with the Panagiotopoulos and Reid mixing rule. Copyright © 2006 Society of Chemical Industry

Tropospheric multiphase chemistry of 2,5- and 2,6-dimethylphenols: determination of the mass accommodation coefficients and the Henry’s law constants

The uptake of 2,5-dimethylphenol and 2,6-dimethylphenol on aqueous surfaces was measured between 279 and 293 K, using the wetted-wall flow tube technique coupled with UV absorption spectroscopic detection. For both compounds, the uptake coefficients gamma were found to be independent of the KOH scavenger concentration in the range of 0.01 to 1 M (pH > pK(a)) and of the liquid-gas contact times. In addition, the uptake coefficients and the derived mass accommodation coefficients alpha show a negative temperature dependence in the investigated temperature range. The mass accommodation coefficients decrease from 1.1 x 10(-3) to 1.1 x 10(-4), and from 5.4 x 10(-4) to 6.4 x 10(-5) for 2,5-dimethylphenol and 2,6-dimethylphenol, respectively. These results are used to discuss the incorporation of these species into the liquid using the nucleation theory. Henry's law constants (HLC) of both compounds were directly measured using a dynamic equilibrium system based on the water/air equilibrium at the interface within the length of a microporous tube. The measurements were conducted over the range 278-293 K in both deionized water and 35 g L(-1) solution of NaCl. At 293 K and in pure water, HLC were found to be equal to (in units of M atm(-1)): 2,5-dimethylphenol, HLC = (1270 +/- 240); 2,6-dimethylphenol, HLC = (250 +/- 80). All of the values for HLC in 35 g L(-1) salt solution were 5-55% lower than the corresponding values in deionized water, depending on the compound and the temperature. These data (mass accommodation coefficients and Henry's law constants) were then used to estimate the partitioning of these phenolic compounds between gaseous and aqueous phases and the corresponding atmospheric lifetimes under clear sky (tau(gas)) and cloudy conditions (tau(multiphase)) have then been derived. The calculated multiphase lifetimes (in units of hours) are lower than those in gas phase at a cumulus temperature of 283 K (in parentheses): 2,5-dimethylphenol, 2.2 (3.5); 2,6-dimethylphenol, 3.8 (4.2).

Morpheeins – a new structural paradigm for allosteric regulation

Classic models for the allosteric regulation of protein function consider an equilibrium among protein structures of constant oligomeric multiplicity. The morpheein (mor-phee'-in) concept expands this model to include a dynamic equilibrium of protein structures wherein a protein monomer can exist in more than one conformation and each monomer conformation dictates a different quaternary structure of finite multiplicity and different functionality. The morpheein concept provides a new framework for understanding allosteric regulation, kinetic cooperativity and hysteresis. Porphobilinogen synthase constitutes a prototype morpheein ensemble comprising several interconverting quaternary structure isoforms; one monomer conformation dictates assembly of a high-activity octamer, whereas an alternative monomer conformation dictates assembly of a low-activity hexamer. It is proposed here that the behavior of some other allosteric enzymes reflect dynamic morpheein equilibrium systems and six candidate proteins are enumerated.

Henry's law constants measurements of the nonylphenol isomer 4(3′,5′-dimethyl-3′-heptyl)-phenol, tertiary octylphenol and γ-hexachlorocyclohexane between 278 and 298 K

Abstract Henry's Law Constants (HLC, M atm−1) were determined for the diastereomeric mixture of the nonylphenol isomer 4(3′,5′-dimethyl-3′-heptyl)-phenol diastereomers (NP353(+) and NP353(−)), tertiary octylphenol (t-OP) and γ-hexachlorocyclohexane (γ-HCH) in artificial seawater over a temperature range 278–298 K using a dynamic equilibrium system. Trace organic substances present in the gas phase were trapped by tandem XAD-2 cartridges and extracted with a soxhlet extractor. The extracts were derivatived with N,O-bis(trimethylsilyl)-trifluoroacetamide (BSTFA), and then analyzed with GC-MS in the selective ion mode. At 293 K and in artificial seawater, HLC (M atm−1) were found to be equal to: NP353(+), HLC=(483±169); NP353(−), HLC=(551±193); t-OP, HLC=(400±140); γ-HCH, HLC=(876±307). The obtained data were used to derive the following Van’t Hoff expressions: ln HLC (NP353(+))=8.73 (±0.95)×(1000/T) –23.61 (±3.30); ln HLC (NP353(–))=8.61 (±0.91)×(1000/T)−23.08 (±3.18); ln HLC (t-OP)=9.03 (±1.40)×(1000/T)−24.83 (±4.86); ln HLC (γ-HCH)=6.17 (±1.08)×(1000/T)−14.28 (±3.75). The derived enthalpies of solvation for NP353(+), NP353(−), t-OP and γ-HCH are −72.6±7.9, −71.6±7.6, −75.1±11.5 and −51.3±9.0 kJ mol−1, respectively. The HLC measurements of γ-HCH, which was used as reference substance, were in good agreement with literature values and its corresponding derived enthalpy of solvation agrees well to the previous values reported in the literature. A reassessment of the air/water gas exchange based on experimentally derived HLC was made for the nonylphenol (NP) in the Lower Hudson River estuary (New York/New Jersey, USA) that was previously reported by Van Ry. A net atmospheric deposition was calculated for the gas exchange of NP in the Lower Bay (Ffw=0.13), and it nearly reaches the condition of equilibrium in the Upper Bay (Ffw=0.46).

Control of a Dynamic Elastic Equilibrium System with Conjugation Conditions

Control of a Dynamic Elastic Equilibrium System with Conjugation Conditions

Uptake Measurements of Dibasic Esters by Water Droplets and Determination of Their Henry's Law Constants

The uptake of dimethyl malonate and dimethyl succinate on aqueous surfaces was measured between 266 and 279 K, using the droplet train technique coupled with mass spectrometric detection. The uptake coefficients A were found to be independent of the aqueous phase composition and of the gas-liquid contact times. In addition, the uptake coefficients and the derived mass accommodation coefficients R show a negative temperature dependence in the temperature ranges studied. The mass accommodations decrease from 7.8 10 -2 to 5.0 10 -2 and from 4.5 10 -2 to 2.3 10 -2 for dimethyl malonate and succinate, respectively. These results are used to discuss the incorporation of oxygenated volatile organic compounds (VOCs) into the liquid using the nucleation theory. Henry’s law constants of both compounds were directly measured between 283 and 298 K using a dynamic equilibrium system. Their values exponentially decrease when temperature increases, from (2.60 ( 0.30) 10 4 to (0.40 ( 0.05) 10 4 and from (1.20 ( 0.10) 10 4 to (0.30 ( 0.03) 10 4 for dimethyl malonate and succinate, respectively (in units of M atm -1 ). The partitioning

Parametric-resonance-induced cable vibrations in network cable-stayed bridges. A continuum approach

There is a wealth of evidence to suggest that the bearing cables of cable-stayed bridges may experience large-amplitude oscillations, attributed in general to parametric resonance with the girder vibrations. A common coutermeasure consists of connecting the principal stays together with secondary cables to form a network and, here, optimal cable arrangments will be discussed when such a network is uniform and triangular meshed. The present approach is qualitative, and basically consists of homogenizing the cable net to an orthotropic elastic membrane, and then considering an auxiliary structure where the bridge girder, instead of being supported by the cable network, is supported by wedge-shaped membranes. The elastic solution under uniformly distributed loads, found using Lekhnitskii's approach, is the starting point for the discussion of the system in dynamic equilibrium. Having established a correspondence between the cable-net size and shape and the elastic moduli of the homogenized membrane, simple formulas are obtained to describe the global bridge vibration, as well as the local oscillations of the cables. It is then possible to estimate the girder and cable-net characteristic frequencies, to evaluate those conditions possibly leading to parametric resonance and, with respect to these variables, to determine optimal cable arrangements. This method is finally applied to the paradigmatic example of the Normandy Bridge.

New possibilities for energy production from renewable low-potential sources

We examine an opportunity for increasing cyclic process efficiency at the expense of taking into account speeds and times of running processes. We consider dynamic equilibrium systems, in which the equations of state include both parameters of the system and environment. At low flow speeds, conventional quasi-static methods apply. At high speeds, new regenerative cycles become possible. This requires the introduction of an extended interpretation of the second law of thermodynamics. This involves specifying the performance of a cycle by the relative difference of temperatures of the working fluid (but not of thermal sources) at the upper and lower temperature levels of the cycle.

The Draco and Ursa Minor Dwarf Spheroidal Galaxies: A Comparative Study

We present (V, I) photometry of two wide (≃25 × 25 arcmin2) fields centered on the low surface brightness dwarf spheroidal galaxies Draco and Ursa Minor. New estimates of the distance to these galaxies are provided [(m-M)0(UMi) = 19.41 ± 0.12 and (m-M)0(Dra) = 19.84 ± 0.14], and a comparative study of their evolved stellar population is presented. We detect for the first time the red giant branch (RGB) bump in the luminosity function of UMi (V = 19.40 ± 0.06), while the feature is not detected in Draco. Photometric metallicity distributions are obtained for the two galaxies, and an accurate analysis to determine the intrinsic metallicity spread is performed by means of artificial star experiments. The adopted method is insensitive to stars more metal poor than [Fe/H] ∼ -2.5, and it rests on the assumption that the age spread in the considered populations is small (i.e., the impact of the actual age spread on the colors of the RGB stars is negligible). We find that while the average metallicity of the two galaxies is similar (⟨[Fe/H]⟩UMi = -1.8 and ⟨Fe/H]⟩Dra = -1.7), the metallicity distributions are significantly different, having different peak values ([Fe/H] = -1.9 and [Fe/H] = -1.6) and different maximum metallicities. We suggest that such differences may be partly responsible for the difference in horizontal-branch morphology between the two galaxies. The intrinsic metallicity 1 σ spread is σi = 0.10 in UMi and σi = 0.13 in Draco. We demonstrate that the inner region of UMi is significantly structured, at odds with what is expected for a system in dynamical equilibrium. In particular, we show that the main density peak of UMi is off-center with respect to the center of symmetry of the whole galaxy and shows a much lower ellipticity with respect to the rest of the galaxy. Moreover, UMi stars are shown to be clustered according to two different characteristic clustering scales, as opposed to Draco, which instead has a very symmetric and smooth density profile. The possible consequences of this striking structural difference on our ideas about galaxy formation are briefly discussed. Combining our distance modulus with the more recent estimates of the total luminosity of UMi, we find that the mass-to-light ratio (M/L) of this galaxy may be as low as M/L ∼ 7, a factor of 5–10 lower than current estimates.

Modeling three-dimensional sculptures of australopithecines (Australopithecus afarensis) for the Museum of Natural History of Vienna (Austria): the post-cranial hypothesis

In March 1999, E. Daynes, a sculptor specializing in fossil hominid reconstruction, asked C. Berge to take over the scientific supervision of the reconstruction of two australopithecine post-crania. The heads had been modeled from two skulls found in Hadar (AL 444-2, AL 417). The sculptures were to be represented in a walking stance. The female proportions (AL 417) are estimated from the skeleton of ‘Lucy’ (AL 288), and the male proportions (AL 444-2) extrapolated from the female ones. Biomechanical and anatomical data (comparison with great apes and humans) are used to reconstruct both dynamic equilibrium and muscular systems. The reconstruction suggests that the fossils moved the pelvis and shoulders extensively when they walked. The hindlimb muscles (such as adductors, gluteal muscles and calf) are fleshy and not or very little tendinous. As indicated by the Laetoli step prints (belonging to a close and contemporaneous species), the foot is adducted during the walk and the support is internal just before take off. In spite of inevitable approximations, such a reconstruction appears to be particularly helpful to bring out morphological and functional traits of the first hominids which are both close to and different from modern humans.

The Nonlinearity and Related Band Strength of Carbon Monoxide When Applied in Ambient Air Measurement Using Open Long-Path Fourier Transform Infrared Spectrometry

ABSTRACT The accuracy of CO concentration determination by open-path Fourier transform infrared (FTIR) spectrometry has been re-evaluated in detail. The evaluation focuses on the correction of the calibration curve—the integrated intensity of a standard spectrum—that is used as a comparison spectrum when doing quantitative analysis of CO. Results show that the calibration curve (with 0.5 cm-1 or 1 cm-1 resolution) is apparently inclined to be nonlinear under standard conditions, and that the threshold point of nonlinearity is ~0.1 atm-cm. Two commercial FTIR field monitoring systems have been used to investigate the nonlinearity trend. The experimental method consists of using open-path FTIR systems in combination with nondispersive infrared (NDIR) monitors to establish the calibration curve in a semi-closed corridor. The results have been double-checked using closed-cell dynamic equilibrium systems. When the optical density is larger than a certain value, the curves begin to bend, and when the optical density approaches zero, the band strength is around 178 ± 3 atm-1 cm-2 and 173 ± 2 atm-1 cm-2, respectively, for 0.5 and 1 cm-1 resolution at standard temperature and pressure (STP). These values are quite different from other published data that have been acquired by the pressurized method or by high-resolution

Henry's Law Constants of Some β-, γ-, and δ-Hydroxy Alkyl Nitrates of Atmospheric Interest

Organic nitrates form via the photodegradation of hydrocarbons in the troposphere in the presence of NO and NO2. This process competes with the chemical cycle leading to ozone production since it sequesters both nitrogen oxides and organic radicals. Hydroxy nitrates form via the atmospheric reactions of alkanes and alkenes and are thought to be an important nitrogen oxides reservoir. In this study, new synthetic methods to produce β-, γ-, and δ-hydroxy nitrates of atmospheric interest were developed. NMR and IR spectroscopies were used to characterize these compounds. Henry's law coefficients of C4 and C5 hydroxy nitrates at 291 ± 2 K were measured using a dynamic equilibrium system. The solubility decreases with the organic chain length and increases with increasing distance between the nitrooxy and hydroxy groups. Due to their large Henry's law coefficients these species will partition into droplets in the presence of clouds and fogs. Measurements of the OH reaction and photolysis rate coefficients are needed for an accurate assessment of the atmospheric lifetimes of these compounds.

Selective Injection of Magnetization by Slow Chemical Exchange in NMR

In a system in slow dynamic equilibrium two NMR methods are shown to be suitable for injecting magnetization from one resonance to another by means of slow chemical exchange. The combined outputs of the methods may be employed to measure the value of the off-rate constant κoff in the complex. The methods are implemented experimentally using the complex of molecules composed of the enzyme Esherichia coli dihydrofolate reductase (DHFR) and the ligand folate. In an equilibrium solution with DHFR, folate is known to undergo chemical exchange between a free state and a bound state. The modified synchronous nutation method is applied to a spin of the folate molecule in the free and bound states; magnetization transfer occurs between the two sites due to the underlying exchange process. As a preliminary step for the application of the synchronous nutation method, a new one-dimensional 1H NMR technique is proposed which facilitates the assignment of the resonance of a spin in the bound state, provided the resonance of its exchange partner in the free state is known. This experiment is also used to obtain quantitative estimates of the transverse relaxation rate constant of the bound resonance. The numerical procedure necessary to analyze the experimental results of the synchronous nutation experiment is presented.

The relaxation of a model system of interacting dipoles

We consider a simple model system of interacting dipoles which can be either free to rotate or trapped, and in which the rotation of a dipole can change the state of neighboring dipoles from trapped to free or vice versa, with probabilities that ensure that the fraction of dipoles that are free remains constant, as is required for systems in dynamic equilibrium. The system was studied in a mean field approximation and also by computer simulations. The results show that the non-exponential decay of the system's response function, and hence of its relaxation function, is associated with the fact that initially the decay is due mainly to the depolarization of the free dipoles, while the later stages are associated with the freeing of the polarized dipoles that were trapped and their subsequent depolarization. This process could be a quite general mechanism for non-exponential dielectric relaxation.