In disperse solution, “osmotic stress” is a restricted case of preferential interactions

In the practice of “osmotic stress,” the effect of excluded cosolvents on a biochemical equilibrium is interpreted as the number of water molecules participating in the reaction. This action is attributed to lowering of solvent water activity by the cosolvent. This concept of osmotic stress in disperse solution is erroneous: (i) A cosolvent cannot be both excluded and inert, i.e., noninteracting, because exclusion requires a positive free energy change; (ii) a decrease in water activity alone by addition of solute cannot affect an equilibrium when the reacting surface is in contact with the solvent; and (iii) osmotic stress in disperse solution is a restricted case of preferential interactions; the reaction is driven by the free energy of cosolvent exclusion, and the derived number of water molecules is solely a measure of the mutual perturbations of the chemical potentials of the cosolvent and the protein.

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.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Isolation and characterization of neutral-lipid-containing organelles and globuli-filled plastids from Brassica napus tapetum

The monolayer tapetum cells of the maturing flowers of Brassica napus contain abundant subcellular globuli-filled plastids and special lipid particles, both enriched with lipids that are supposed to be discharged and deposited onto the surface of adjacent maturing pollen. We separated the two organelles by flotation density gradient centrifugation and identified them by electron microscopy. The globuli-filled plastids had a morphology similar to those described in other plant species and tissues. They had an equilibrium density of 1.02 g/cm3 and contained neutral esters and unique polypeptides. The lipid particles contained patches of osmiophilic materials situated among densely packed vesicles and did not have an enclosing membrane. They exhibited osmotic properties, presumably exerted by the individual vesicles. They had an equilibrium density of 1.05 g/cm3 and possessed triacylglycerols and unique polypeptides. Several of these polypeptides were identified, by their N-terminal sequences or antibody cross-reactivity, as oleosins, proteins known to be associated with seed storage oil bodies. The morphological and biochemical characteristics of the lipid particles indicate that they are novel organelles in eukaryotes that have not been previously isolated and studied. After lysis of the tapetum cells at a late stage of floral development, only the major plastid neutral ester was recovered, whereas the other abundant lipids and proteins of the two tapetum organelles were present in fragmented forms or absent on the pollen surface.

Equilibrium constants and free energies in unfolding of proteins in urea solutions

A novel thermodynamic approach to the reversible unfolding of proteins in aqueous urea solutions has been developed based on the premise that urea ligands are bound cooperatively to the macromolecule. When successive stoichiometric binding constants have values larger than expected from statistical effects, an equation for moles of bound urea can be derived that contains imaginary terms. For a very steep unfolding curve, one can then show that the fraction of protein unfolded, B̄, depends on the square of the urea concentration, U, and is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\bar {B}=\frac{{\mathit{A}}^{{\mathit{2}}}_{{\mathit{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}n\bar {B}}{\mathit{U}}^{{\mathit{2}}}}{{\mathrm{1\hspace{.167em}+\hspace{.167em}}}{\mathit{A}}^{{\mathrm{2}}}_{{\mathrm{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}\bar {B}}{\mathit{U}}^{{\mathrm{2}}}}{\mathrm{.}}\end{equation*}\end{document} A12 is the binding constant as B̄→ 0, and λ is a parameter that reflects the augmentation in affinities of protein for urea as the moles bound increases to the saturation number, n. This equation provides an analytic expression that reproduces the unfolding curve with good precision, suggests a simple linear graphical procedure for evaluating A12 and λ, and leads to the appropriate standard free energy changes. The calculated ΔG° values reflect the coupling of urea binding with unfolding of the protein. Some possible implications of this analysis to protein folding in vivo are described.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

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.

Changes in brain cell shape create residual extracellular space volume and explain tortuosity behavior during osmotic challenge

Diffusion of molecules in brain extracellular space is constrained by two macroscopic parameters, tortuosity factor λ and volume fraction α. Recent studies in brain slices show that when osmolarity is reduced, λ increases while α decreases. In contrast, with increased osmolarity, α increases, but λ attains a plateau. Using homogenization theory and a variety of lattice models, we found that the plateau behavior of λ can be explained if the shape of brain cells changes nonuniformly during the shrinking or swelling induced by osmotic challenge. The nonuniform cellular shrinkage creates residual extracellular space that temporarily traps diffusing molecules, thus impeding the macroscopic diffusion. The paper also discusses the definition of tortuosity and its independence of the measurement frame of reference.

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.

Local osmotic gradients drive the water flux associated with Na+/glucose cotransport

It recently was proposed [Loo, D. D. F., Zeuthen, T., Chandy, G. & Wright, E. M. (1996) Proc. Natl. Acad. Sci. USA 93, 13367–13370] that SGLT1, the high affinity intestinal and renal sodium/glucose cotransporter carries water molecules along with the cosubstrates with a strict stoichiometry of two Na+, one glucose, and ≈220 water molecules per transport cycle. Using electrophysiology together with sensitive volumetric measurements, we investigated the nature of the driving force behind the cotransporter-mediated water flux. The osmotic water permeability of oocytes expressing human SGLT1 (Lp ± SE) averaged 3.8 ± 0.3 × 10−4 cm⋅s−1 (n = 15) and addition of 100 μM phlorizin (a specific SGLT1 inhibitor) reduced the permeability to 2.2 ± 0.2 × 10−4 cm⋅s−1 (n = 15), confirming the presence of a significant water permeability closely associated with the cotransporter. Addition of 5 mM α-methyl-glucose (αMG) induced an average inward current of 800 ± 10 nA at −50 mV and a water influx reaching 120 ± 20 pL cm−2 ⋅s−1 within 5–8 min. After rapidly inhibiting the Na+/glucose cotransport with phlorizin, the water flux remained significantly elevated, clearly indicating the presence of a local osmotic gradient (Δπ) estimated at 16 ± 2 mOsm. In short-term experiments, a rapid depolarization from −100 to 0 mV in the presence of αMG decreased the cotransport current by 94% but failed to produce a comparable reduction in the swelling rate. A mathematical model depicting the intracellular accumulation of transported osmolytes can accurately account for these observations. It is concluded that, in SGLT1-expressing oocytes, αMG-dependent water influx is induced by a local osmotic gradient by using both endogenous and SGLT1-dependent water permeability.

Root Xylem Embolisms and Refilling. Relation to Water Potentials of Soil, Roots, and Leaves, and Osmotic Potentials of Root Xylem Sap1

Embolism and refilling of vessels was monitored directly by cryomicroscopy of field-grown corn (Zea mays L.) roots. To test the reliability of an earlier study showing embolism refilling in roots at negative leaf water potentials, embolisms were counted, and root water potentials (Ψroot) and osmotic potentials of exuded xylem sap from the same roots were measured by isopiestic psychrometry. All vessels were full at dawn (Ψroot −0.1 MPa). Embolisms were first seen in late metaxylem vessels at 8 am. Embolized late metaxylem vessels peaked at 50% at 10 am (Ψroot −0.1 MPa), fell to 44% by 12 pm (Ψroot −0.23 MPa), then dropped steadily to zero by early evening (Ψroot −0.28 MPa). Transpiration was highest (8.5 μg cm−2 s−1) between 12 and 2 pm when the percentage of vessels embolized was falling. Embolized vessels were refilled by liquid moving through their lateral walls. Xylem sap was very low in solutes. The mechanism of vessel refilling, when Ψroot is negative, requires further investigation. Daily embolism and refilling in roots of well-watered plants is a normal occurrence and may be a component of an important hydraulic signaling mechanism between roots and shoots.

Osmotic Water Permeability of Isolated Protoplasts. Modifications during Development1

A transference chamber was developed to measure the osmotic water permeability coefficient (Pos) in protoplasts 40 to 120 μm in diameter. The protoplast was held by a micropipette and submitted to a steep osmotic gradient created in the transference chamber. Pos was derived from the changes in protoplast dimensions, as measured using a light microscope. Permeabilities were in the range 1 to 1000 μm s−1 for the various types of protoplasts tested. The precision for Pos was ≤40%, and within this limit, no asymmetry in the water fluxes was observed. Measurements on protoplasts isolated from 2- to 5-d-old roots revealed a dramatic increase in Pos during root development. A shift in Pos from 10 to 500 μm s−1 occurred within less than 48 h. This phenomenon was found in maize (Zea mays), wheat (Triticum aestivum), and rape (Brassica napus) roots. These results show that early developmental processes modify water-transport properties of the plasma membrane, and that the transference chamber is adapted to the study of water-transport mechanisms in native membranes.