Equilibrium Of Molecules Research Articles

Detection of rare partially folded molecules in equilibrium with the native conformation of RNaseH.

Despite the general observation that single domain proteins denature in a completely cooperative manner, amide hydrogen exchange of ribonuclease H in low levels of denaturant demonstrates the existence of two partially folded species. The structures of these marginally stable species resemble kinetic folding intermediates and the molten globule state of the protein. These data suggest that the first region to fold is the thermodynamically most stable portion of the protein and that the molten globule is a high free energy conformation present at equilibrium in the native state.

Unesterified cholesterol content of human sperm regulates the response of the acrosome to the agonist, progesterone.

Human sperm become responsive to inducers of the acrosome reaction if they are washed free of seminal plasma and incubated in an appropriate medium. We tested the hypothesis that sperm must lose cholesterol during incubation in order to become responsive to the agonist, progesterone. Freshly ejaculated sperm contained 2.92 +/- 0.202 nmol unesterified cholesterol/10(7) sperm (mean +/- SEM, n = 18). When incubated for 24 h in vitro, sperm suspensions lost 29 +/- 6% of their free cholesterol (n = 23). Sperm lost cholesterol slightly faster than they became acrosomally responsive. Adding cholesterol to the medium prevented sperm from losing cholesterol and from becoming responsive. Varying the cholesterol content of the medium had similar effects on loss of sperm cholesterol (ED50 = 406 nM) and acrosomal responsiveness (ED50 = 388 nM). Incubating sperm with a 1:150 dilution of seminal plasma (containing 5.18 microM cholesterol) also prevented sperm from losing cholesterol and from becoming responsive. Incubating sperm 24 h in medium containing 0.5 mg/ml phosphatidylcholine increased the amount of cholesterol lost and the number of sperm that became responsive. Our results support a model in which sperm unesterified cholesterol (or a molecule in equilibrium with it) suppresses acrosomal responsiveness. Sperm must lose unesterified cholesterol to become responsive to progesterone.

The human immunodeficiency virus type 1 transmembrane gp41 protein is a calcium-binding protein and interacts with the putative second-receptor molecules in a calcium-dependent manner

Fusion is a crucial event in the life cycle of the human immunodeficiency virus (HIV); is is initiated by the high-affinity binding between gp120, the external surface glycoprotein of HIV-1, and the differentiation antigen CD4 and finally results in the insertion of the hydrophobic amino terminus of the gp41 envelope glycoprotein into the plasma membrane of the target cell. Recent results suggest that this process is dependent upon calcium ions, but the mechanism or the proteins involved are not understood. Computer-assisted sequence analysis revealed a putative calcium-binding site within the extracellular part of gp41 that was highly reminiscent of the calcium-binding EF-hand structure. To test this hypothesis, calcium-binding experiments were performed. Binding of a recombinant soluble form of the transmembrane protein (rsgp41) to its putative second-receptor molecules in equilibrium was dependent upon calcium. The affinity was not influenced by calcium, but the maximum binding was increased in a dose-dependent manner. Radioactive calcium bound to rsgp41 covalently attached to Sepharose but not to bovine serum albumin. Binding was inhibited by the addition of nonradioactive calcium, indicating that binding was specific. Neither magnesium nor manganese inhibited the binding of labeled calcium to rsgp41. Binding was dependent on the oxidative state of the rsgp41 molecule, suggesting the functional importance of the correctly folded structure of the rsgp41 protein. In this report, we demonstrate that the HIV-1 transmembrane protein gp41 is a calcium-binding protein and interacts with the putative second-receptor molecules in a calcium-dependent manner.

Formation and scission of the sulfur–sulfur bond: a new approach to reactions between sulfur/polysulfide ions and thiolate ions/disulfides in N,N-dimethylacetamide

The reactivity of sulfur towards a series of thiolate ions RS–[R = phenyl (1), 4-methylphenyl (2), benzyl (3) ethyl (4), propyl (5), butyl (6), sec-butyl (7), tert-butyl (8)] has been studied by spectroelectrochemistry in N,N-dimethylacetamide. Apparently, sulfur reacts in two parallel ways: (i) oxidation of RS– leading to RS2R and S3˙– ions; (ii) preponderant S-nucleophilic process yielding stable RSx– ions (x= 2–5). RSx– species, whose spectrophotometric characteristics have been determined, are successively obtained in the course of sulfur addition with R = alkyl, whereas equilibria between arylpolysulfide ions were observed. At the junction of these two parallel pathways, the slow key equilibrium 2RS4–⇌ RS2R + 2S3˙– has been investigated by addition of RS2R R = 1–8 to S3˙– solutions. In fact, our study is consistent with at first, a monoelectronic transfer between RS–(or RS2–) ions and the very reactive S2 molecules in equilibrium with S8. The fast and competing couplings of the radicals RS˙(or RS2˙), S2˙–(or S3˙–) agree with the simultaneous formation of RS2R, RSx– and polysulfide ions. More generally, the S2/S2˙– redox system is believed to be involved in thiophilic reactions of a number of anions such as RS– towards sulfur rather than the initial opening of the cyclic S8 form.

Determination of Ion−Solvent Equilibria in the Gas Phase. Hydration of Diprotonated Diamines and Bis(trimethylammonium) Alkanes

Many ions of interest in condensed phase chemistry cannot be produced in the gas phase by conventional methods. This is particularly the case for multiply charged inorganic and bio-organic ions. However, these species can be produced by electrospray, which is a method with which electrolyte ions present in a solution can be transferred to the gas phase. An ion-source reaction chamber was developed with which the equilibrium constants of ion−molecule equilibria and their temperature dependence can be determined, where the ions involved are produced by electrospray. The hydration equilibria Mz+(H2O)n-1 + H2O = Mz+(H2O)n were determined for Mz+ = Na+, K+, n-C3H7NH3+, n-C6H13NH3+. The ΔG°n-1,n, ΔH°n-1,n, and ΔS°n-1,n were found to be in good agreement with previous determinations where these ions were produced by conventional techniques. Equilibria determinations were also obtained for the diprotonated α,ω-alkyldiammonium ions: H3N(CH2)pNH32+ where p = 5, 6, 7, 8, 9, 10, 12. The ΔH° values obtained for these...

A novel method for determining absolute coverages by temperature programmed desorption with application to the adsorption of CH 3I on MgO(100)

A new method is presented for conveniently determining the absolute coverage of molecular overlayers on solid surfaces using only temperature programmed desorption (TPD), i.e. no additional measurement techniques must be employed. The method is based on a calibration of the measured mass spectrometer signal during evaporation from multilayers of the adsorbate using an a priori calculation of the evaporation flux. The computation of the evaporation flux requires a knowledge of the molecule's equilibrium vapor pressure at the evaporation temperature and an assumption of near unity trapping/sticking probability for the vapor impinging on the condensed layer at this temperature. The method is illustrated using TPD of methyl iodide from the MgO(100) surface. Significant features in the TPD are discussed in light of the methyl iodide coverages obtained using the method.

The electrochemical reduction of iron porphyrin nitrosyls in the presence of weak acids

The reduction of coordinated nitrosyls to ammonia in assimilatory nitrite reductases consists of a series of electron transfer/ protonation steps. Very little detail is known about these steps, either from the enzyme itself or model complexes. In this work, the mechanism for the reduction of iron nitrosyl complexes, which are nitrite reductase models, was examined in solutions with limited proton availability. In this way, the reduction mechanism can be investigated in a system which has been shown quantitatively to produce ammonia. The reduction mechanism was investigated for the reduction of Fe(P)(NO), where P is porphyrins, hydroporphyrins or oxoporphyrins, in the presence of substituted phenols using pulse polarography. In THF, the limiting current for the first wave (wave I) was unaffected by the presence of phenol, while the half-wave potential shifted to positive potentials at high concentrations of phenol. The shift in E 1 2 of the first wave, E 1 2 ,I , was consistent with a mechanism which involved the protonation of Fe(TPP)(NO) − with two protons to form Fe(TPP)(NH 2O +). From the variation in the half-wave potential, the equilibrium constant for the formation of Fe(TPP)(NH 2O +) from Fe(TPP)(NO) − was measured for a series of phenols. The chemical and electrochemical reversibility of the first wave in the presence of phenol was verified by the Nernstian shape of the waves, by square-wave voltammetry, and by shifts caused by the presence of phenolate ion. The reduction in the presence of 2,6-dichlorophenol was an exception in that only one proton was transferred. In addition to the changes in the first wave, a new wave was observed between the first and second waves of Fe(TPP)(NO). This new wave corresponded to a three-electron reduction of Fe(TPP)(NO) −. The kinetics of this reduction were monitored using normal pulse polarography. The behavior of the new wave in the presence of phenol was consistent with a CE mechanism which involved two phenol molecules in equilibrium with Fe(TPP)(NO) − to form Fe(TPP)(NH 2O +) prior to the electron transfer. The rate constant for the reduction was measured for all the phenols for which the equilibrium constant for the formation of Fe(TPP)(NH 2O +) could be measured. Changes in the macrocycle from porphyrin to isobacteriochlorin led to a significant increase in the rate of nitrosyl reduction, while the rate decreased substantially for the oxoporphyrins. Most of the changes in the rate of nitrosyl reduction were consistent with changes in the basicity of the Fe(P)(NO) − complex. It is interesting to note that Fe(P)(NH 2O +), the reactive intermediate, was formed most readily for the assimilatory nitrite reductase models (iron isobacteriochlorins), and least readily for the dissimilatory nitrite reductase models (iron dioxo-isobacteriochlorin).

Polycaprolactone-based block copolymers: 4. Interfacial activity in poly(vinyl chloride) containing polyblends

The substantial difference in the T g of poly(vinyl chloride) (PVC) and poly(ε-caprolactone) (PCL) offers a sensitive method of locating a polystyrene (PS)-PCL diblock in PVC or in PS/PVC polyblends. When mixed with PVC, these diblocks are dispersed as individual molecules in equilibrium with micelles. The equilibrium position depends on the composition of the diblock; when PCL is the major component, molecular dissolution in PVC is enhanced. A 50 50 PS-PCL diblock, each block of which is of a higher molecular weight than the related homopolymer, is located mainly at the PS/PVC interface, as shown by the essentially unchanged T g of the PVC matrix and a sub- T g assigned to the external layer of the PVC phases plasticized by the PCL blocks of the copolymer. Blocks longer than the associated homopolymer chain clearly enhance the mutual anchoring of the PS and PVC phases. Since PS and PVC are intrinsically brittle polymers, their melt blending in the presence of properly designed PS-PCL diblocks gives rise to fragile materials.

An optimal formulation of the matrix method in statistical mechanics of one‐dimensional interacting units: Efficient iterative algorithmic procedures

AbstractStatistical mechanical calculations for one‐dimensional interacting units have undergone great development in many fields of macromolecular science. The partition function is the most rigorous description of an ensemble of molecules in equilibrium. Specific methodological formulations and algorithms were developed to handle numerically the inclusion of long‐range effects (as compared to usual nearest neighbor Ising models) and known sequence‐dependent heterogeneities of biological macromolecules. The most successful approach in formulating these problems in a very general and tractable framework was the so‐called matrix method. Despite several improvements, it was claimed that in practical applications this approach had fundamental limitations inherent to any “matrix” formulation. We show here that a new conceptual formulation allows us to overcome these limitations completely. We propose a general iterative procedure that combines the theoretical advantages of the matrix method with the possibility of highly optimized and efficient numerical algorithms.

Complex kinetic systems with time-dependent rate coefficients

Analysis of different models available to treat complex kinetic systems with time-dependent rate coefficients was performed. The differential model (D), the superposition model (S), and the convolution model (C) were applied to a kinetic scheme describing two excited molecules in equilibrium that can also undergo diffusion-controlled quenching processes with another species. All the models predict similar results when the equilibrium is slow. However, large differences were obtained between the convolution model and the other ones in the case of fast equilibrium. Difference between models are explained in terms of the influence of the re-excitation term on the evolution of the distribution functions in the course of the quenching processes.

On the Law of Equipartition for Translational Motion of Excited Molecules in Equilibrium with Thermal Radiation

Abstract Einstein’s radiation theory consists of two parts: the derivation of Planck's radiation law from a physical mechanism of absorption and emission of radiation by excited molecules that are in thermal equilibrium with the radiation field and a demonstration of the validity of the law of equipartition of energy for the translational motion of the molecules. Several incongruities are observed: Einstein could not have legitimately substituted back into his dynamical equilibrium condition, valid at any finite temperature, a limiting condition between the coefficients of absorption and stimulated emission that he obtained in the high temperature limit. His justification of the law of equipartition involves, on the one hand, treating the motion of the excited molecule as brownian motion while, on the other hand, employing special relativity to obtain an expression for the diffusion coefficient. In the former the velocity of the molecule is a stochastic variable while in the latter it is a uniform velocity. Hence equipartition does not hold for the translational motion.

Thermodynamics of the sublimation of thallium(I) fluoride by simultaneous Knudsen-effusion and torsion-effusion

The partial vapor pressures of monomeric and dimeric molecules in equilibrium with solid thallium(I) fluoride were measured by simultaneous Knudsen-effusion and torsion-effusion in the temperature range 516 to 572 K. The partial pressures of TlF(g) and Tl 2F 2(g) are expressed by: ln( p m p o ) = A − B( K T ) . The values of A and B are given. The calculated partial pressures established that the dimer constitutes 43 moles per cent of the equilibrium vapor. The third-law values of the standard molar enthalpies of sublimation Δ sub H m o(298.15 K) are (139.9±5.0) and (148.8±5.0) kJ·mol −1 for TlF(g) and Tl 2F 2(g), respectively. The third-law standard molar enthalpy change for the dissociation: Tl 2F 2(g) = 2TlF(g) is Δ r H m o(298.15 K) = (131±5) kJ·mol −1.

Immunoglobulin surface-binding kinetics studied by total internal reflection with fluorescence correlation spectroscopy

An experimental application of total internal reflection with fluorescence correlation spectroscopy (TIR/FCS) is presented. TIR/FCS is a new technique for measuring the binding and unbinding rates and surface diffusion coefficient of fluorescent-labeled solute molecules in equilibrium at a surface. A laser beam totally internally reflects at the solid-liquid interface, selectively exciting surface-adsorbed molecules. Fluorescence collected by a microscope from a small, well-defined surface area approximately 5 micron2 spontaneously fluctuates as solute molecules randomly bind to, unbind from, and/or diffuse along the surface in chemical equilibrium. The fluorescence is detected by a photomultiplier and autocorrelated on-line by a minicomputer. The shape of the autocorrelation function depends on the bulk and surface diffusion coefficients, the binding rate constants, and the shape of the illuminated and observed region. The normalized amplitude of the autocorrelation function depends on the average number of molecules bound within the observed area. TIR/FCS requires no spectroscopic or thermodynamic change between dissociated and complexed states and no extrinsic perturbation from equilibrium. Using TIR/FCS, we determine that rhodamine-labeled immunoglobulin and insulin each nonspecifically adsorb to serum albumin-coated fused silica with both reversible and irreversible components. The characteristic time of the most rapidly reversible component measured is approximately 5 ms and is limited by the rate of bulk diffusion. Rhodamine-labeled bivalent antibodies to dinitrophenyl (DNP) bind to DNP-coated fused silica virtually irreversibly. Univalent Fab fragments of these same antibodies appear to specifically bind to DNP-coated fused silica, accompanied by a large amount of nonspecific binding. TIR/FCS is shown to be a feasible technique for measuring absorption/desorption kinetic rates at equilibrium. In suitable systems where nonspecific binding is low, TIR/FCS should prove useful for measuring specific solute-surface kinetic rates.

Kinetic evidence for a conformation change of tubulin preceding microtubule assembly.

The assembly of microtubule protein has been investigated under conditions where the microtubule seeds concentration was varied. The plot of the apparent first order elongation rate constant with microtubule number concentration strongly deviated from the linearity predicted by Oosawa's condensation model and reached a limit at a high concentration of seeds. The increase in seeds concentration was quantitatively assessed from the histograms of microtubule length distribution and from the parallel increases in the rate of depolymerization at 4 degrees C and steady state rate of GTP hydrolysis at microtubule ends. The limit elongation rate constant was independent of elongating sites and tubulin concentrations and was attributed to the true first order rate constant of a conformation change of tubulin preceding its assembly in microtubules. It is hypothesized that polymerizable tubulin would represent a small fraction only of the tubulin molecules in equilibrium with unpolymerizable species. Microtubule assembly would follow the shift of this equilibrium which is fast as compared to the rate of polymerization at low concentration of elongating sites but becomes rate limiting at higher concentrations.

Developments in the theory of cationic polymerization-VII [1a,b]: Theoretical attempts at improving initiators for cationic polymerization of alkenes

The initiation of the cationic polymerisation of alkenes is examined in detail by means of simple thermodynamic concepts. From a consideration of the kinetic requirements it is shown that the ideal initiator will yield a stable, singly charged anion and a cation with a high reactivity towards the monomer by simple, well defined reactions. It must also be adequately soluble in the solvent of choice and for the experimental method to be used. The calculations are applied to carbocation salts as initiators and a method of predicting their relative solubilities is described. From established and predicted data for a variety of carbocation salts the position of their ion:molecule equilibria and their reactivity towards alkenes are examined by means of Born-Haber cycles. This treatment established the relative stabilities of a number of anions and the reason for dityl, but not trityl salts initiating the polymerisation of isobutene. The outcome of our treatment is a general method for selecting theoretically promising new initiators.

A mean-field model of the alkane-saturated lipid bilayer above its phase transition. I. Development of the model

A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules in equilibrium with an aqueous phase saturated with an n-alkane is presented. A mean-field approach developed in previous work on a solventless bilayer (Gruen, Biochim. Biophys. Acta. 595:161--183, 1980) is extended to allow alkane chains to exist in the hydrophobic core of the membrane. As the alkane chains are chemically similar to the lipid chains, much of the analysis follows directly from the solventless model. Novel features of the present model are the inclusion of (a) a term which models the free energy cost of creating space for alkane conformations, (b) a term which constrains the chains to pack evenly in the hydrophobic region of the membrane, and (c) a term which estimates the free energy of mixing of the lipid and alkane molecules in the plane of the bilayer. On uptake of alkane, the dimensions of the bilayer increase. Allowance is made for an increase in thickness and/or an increase in area per lipid. A thermodynamic framework is established which allows evaluation of the free energy of a bilayer of arbitrary dimensions with a view to predicting the equilibrium structure.

Tactoidal state and phase transitions in systems of linear polymers of variable length

The tactoidal state in systems containing long, rod-like molecules consists of partially aligned solute molecules in equilibrium with and at a concentration not much higher than that in the conjugate isotropic phase. Under the liquid lattice model of Flory [Proc. R. Soc. London Ser. A, (1956) 234, 73-89], as well as under other models, tactoid formation by molecules of fixed axial ratio depends on nonideality induced by excluded volumes; the process is wholly entropy driven and requires no direct interactions between rods. Many rod-like biological polymers exhibit reversible polymerization, so that axial ratio and length are not fixed. Polymerization and rod length will then not only induce nonideality, alignment, and phase separation, but will be affected by these. In this work these interrelations are treated under the model of Flory, modified to include a free energy of polymerization and to permit reversible changes in rod length. The primary conclusion is that, in contrast to the situation for fixed lengths, excluded volume-dependent nonideality alone does not suffice to induce a tactoidal phase separation. In the absence of attractions or repulsions between rods the anisotropic phase is highly concentrated. This phase only becomes tactoidal when a minimal level of repulsive interaction between rods is reached. Under this model, tactoid formation in systems such as deoxygenated hemoglobin S and tobacco mosaic virus depends on repulsive interactions or metastability or both. As a secondary result it is shown that rod length in the anisotropic phase is much greater than in the conjugate isotropic phase.

Far Infrared Spectroscopic Studies of Acetonitrile Vapour

Abstract The infrared spectrum of acetonitrile vapour has been obtained in the range below 100 cm−1. There is an absorption band located at 78 cm−1 which is assigned to overlapping intermolecular vibrations of dimer molecules in equilibrium with the monomer species. The equilibrium constant calculated from the pressure dependence of the band intensity amounts to 42 ± 26 1·mol−1.

Factors influencing the percutaneous absorption of drugs.

The skin is the most readily accessible organ of the human body; only a fraction of a millimeter separates its surface from the underlying capillary network. Yet, skin protects superbly against damage by micro- and macro-molecular entities, as well as against uncontrolled loss of vital biological substances, by virtue of its astonishingly low permeability to such substances. We have reexamined and attempted to reconcile the barrier characteristics of skin in terms not only of its composition and microstructure, but also of present understanding of membrane permeability and permselectivity. The principal barrier to percutaneous transport is localized within the stratum corneum. We have developed a mathematical model of this tissue as a two-phase protein-lipid heterogeneous membrane, which correlates the permeability of the membrane to a specific penetrant with the water solubility of the penetrant and with its lipid-protein partition coefficient. We have also found that a simplistic model of the sorption process, which invokes the coexistence of dissolved and mobile sorbed molecules in equilibrium with site-bound and immobile molecules within the membrane, accurately correlates experimental sorption data and transient transport measurements. The interstitial lipid phase of the stratum corneum is the cause of the exceedingly low, apparent diffusivity of drugs (e.g. scopolamine) and, in this regard, acts as the principal permeation barrier, whereas the drug sorbed by the stratum corneum is localized predominantly within the protein phase of the tissue. We have also found that the effects of the permeation adjuvant, dimethyl sulfoxide, on skin permeability are entirely consistent with accepted sorption-diffusion models of membrane transport, when changes in penetrant activity with changes in solvent composition and tissue microstructure induced by osmotic shock are properly allowed for.

Conformational analysis—132: The effects of electrostatic interactions and solvation energies on conformational equilibria in dihalides and haloketones Tetrahedron 34, 627, 1978.

A preliminary study of the effect of solvation on conformational equilibria in molecules containing two or more polar groups has been carried out within the framework of the molecular mechanics method. The procedure consists of placing standard point charges at nuclei, and allowing for the induced charges by the modified Smith-Eyring method. The molecular dipole and quadrupole are then calculated, and their solvation energies are found using effective dielectric constants for common solvents. The results are on the whole satisfactory.