V. Adrian Parsegian

Electrostatic potential between surfaces bearing ionizable groups in ionic equilibrium with physiologic saline solution

Abstract In the past calculations of electrostatic properties of interacting cellular surfaces have been restricted by assumptions of fixed surface charge or surface potential. For the most part these calculations have been confined to a linear approximation and neglect the small but important complement of divalent cations in the cellular environment. In the present paper these limitations are removed. Solutions are obtained to the full non-linear Poisson-Boltzmann equation, treating the fraction of dissociated ionizable surface groups as a self-consistent functional of the electrostatic potential. The potential is expressed in terms of relations between Jacobian elliptic functions. A general and efficient method of computation is developed through the theory of Jacobian theta functions. The treatment given here offers wide flexibility in dealing with cell surfaces in the languages of the cell physiologist, biochemist and physical chemist.

[3] Macromolecules and water: Probing with osmotic stress

Publisher Summary This chapter presents specific examples to describe procedures and use osmotic stress with maximum ease and efficiency. These examples are systems where intentionally varied water activity has revealed a connection between different functional states of proteins or other large molecules with different amounts of water associated with them. The method––osmotic stress on macromolecules–– is applied to four kinds of processes, which are (1) ionic channel opening/closing, (2) enzyme/ substrate association and turnover, (3) molecular binding, and (4) longrange interaction. Through these examples, a thermodynamic relations is developed that is useful in the interpretation of osmotic stress data. Osmotic stress experiments, in explicitly recognizing the importance of water activity, are designed to buffer it so that it is as well defined as other more familiar solution variables. Osmotic stress measurements have revealed a surprisingly large influence of water activity on macromolecular reactions and conformational transitions. It even appears that small solutes, typically thought to affect macromolecules only through direct binding, show an indirect effect through their influence on water activity.

Measured long-range repulsive Casimir-Lifshitz forces.

Quantum fluctuations create intermolecular forces that pervade macroscopic bodies. At molecular separations of a few nanometres or less, these interactions are the familiar van der Waals forces. However, as recognized in the theories of Casimir, Polder and Lifshitz, at larger distances and between macroscopic condensed media they reveal retardation effects associated with the finite speed of light. Although these long-range forces exist within all matter, only attractive interactions have so far been measured between material bodies. Here we show experimentally that, in accord with theoretical prediction, the sign of the force can be changed from attractive to repulsive by suitable choice of interacting materials immersed in a fluid. The measured repulsive interaction is found to be weaker than the attractive. However, in both cases the magnitude of the force increases with decreasing surface separation. Repulsive Casimir–Lifshitz forces could allow quantum levitation of objects in a fluid and lead to a new class of switchable nanoscale devices with ultra-low static friction.

Structure and Fluctuations of Charged Phosphatidylserine Bilayers in the Absence of Salt

Using x-ray diffraction and NMR spectroscopy, we present structural and material properties of phosphatidylserine (PS) bilayers that may account for the well documented implications of PS headgroups in cell activity. At 30 degrees C, the 18-carbon monounsaturated DOPS in the fluid state has a cross-sectional area of 65.3 A(2) which is remarkably smaller than the area 72.5 A(2) of the DOPC analog, despite the extra electrostatic repulsion expected for charged PS headgroups. Similarly, at 20 degrees C, the 14-carbon disaturated DMPS in the gel phase has an area of 40.8 A(2) vs. 48.1 A(2) for DMPC. This condensation of area suggests an extra attractive interaction, perhaps hydrogen bonding, between PS headgroups. Unlike zwitterionic lipids, stacks of PS bilayers swell indefinitely as water is added. Data obtained for osmotic pressure versus interbilayer water spacing for fluid phase DOPS are well fit by electrostatic interactions calculated for the Gouy-Chapman regime. It is shown that the electrostatic interactions completely dominate the fluctuational pressure. Nevertheless, the x-ray data definitively exhibit the effects of fluctuations in fluid phase DOPS. From our measurements of fluctuations, we obtain the product of the bilayer bending modulus K(C) and the smectic compression modulus B. At the same interbilayer separation, the interbilayer fluctuations are smaller in DOPS than for DOPC, showing that B and/or K(C) are larger. Complementing the x-ray data, (31)P-chemical shift anisotropy measured by NMR suggest that the DOPS headgroups are less sensitive to osmotic pressure than DOPC headgroups, which is consistent with a larger K(C) in DOPS. Quadrupolar splittings for D(2)O decay less rapidly with increasing water content for DOPS than for DOPC, indicating greater perturbation of interlamellar water and suggesting a greater interlamellar hydration force in DOPS. Our comparisons between bilayers of PS and PC lipids with the same chains and the same temperature enable us to focus on the effects of these headgroups on bilayer properties.

ON THE ELECTROSTATIC INTERACTION ACROSS A SALT SOLUTION BETWEEN TWO BODIES BEARING UNEQUAL CHARGES

We consider two parallel planar charged surfaces bearing unequal surface charge densities interacting across a region in ionic equilibrium with a neutral salt solution. Combining rules are derived appropriate for interactions across distances of separation greater than the characteristic Debye length. When ions are excluded from the regions behind the interacting surfaces there can be repulsion between charged surfaces of opposite sign; but surfaces bearing charges of the same sign never attract one another. Also, surfaces bearing electrostatic potential of like sign can attract.

Swelling of phospholipids by monovalent salt

Critical to biological processes such as membrane fusion and secretion, ion-lipid interactions at the membrane-water interface still raise many unanswered questions. Using reconstituted phosphatidylcholine membranes, we confirm here that multilamellar vesicles swell in salt solutions, a direct indication that salt modifies the interactions between neighboring membranes. By varying sample histories, and by comparing with data from ion carrier-containing bilayers, we eliminate the possibility that swelling is an equilibration artifact. Although both attractive and repulsive forces could be modified by salt, we show experimentally that swelling is driven primarily by weakening of the van der Waals attraction. To isolate the effect of salt on van der Waals interactions, we focus on high salt concentrations at which any possible electrostatic interactions are screened. By analysis of X-ray diffraction data, we show that salt does not alter membrane structure or bending rigidity, eliminating the possibility that repulsive fluctuation forces change with salt. By measuring changes in interbilayer separation with applied osmotic stress, we have determined, using the standard paradigm for bilayer interactions, that 1 M concentrations of KBr or KCl decrease the van der Waals strength by 50%. By weakening van der Waals attractions, salt increases energy barriers to membrane contact, possibly affecting cellular communication and biological signaling.

DNA-DNA interactions

The forces that govern DNA double helix organization are being finally systematically measured. The non-specific longer-range interactions--such as electrostatic interactions, hydration, and fluctuation forces--that treat DNA as a featureless rod are reasonably well recognized. Recently, specific interactions--such as those controlled by condensing agents or those consequent to helical structure-are beginning to be recognized, quantified and tested.

Attractive forces between cation condensed DNA double helices.

By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 +/- 0.1 A characteristic decay length and the attractive component of the free energy is always 2.3 +/- 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 +/- 0.5 A characteristic decay length for intermolecular attractions between condensed DNA molecules.

A PHYSICAL METHOD FOR DERIVING THE ELECTROSTATIC INTERACTION BETWEEN ROD-LIKE POLYIONS AT ALL MUTUAL ANGLES

The screened Coulomb interaction between polyelectrolyte cylinders immersed in an ionic bath is examined. The electrostatic force and torque acting between a pair of unlike rods is formulated for all separations in which the electrostatic potential on some dividing surface between rods can be written as a linear superposition of isolated cylinder potentials. (The surface potential on the rods themselves may be much higher than that permitted by a superposition approximation.) The mutual energy in the case of skewed rods is found to be exponential in separation and proportional to 1/sin theta where theta is the twist angle of one rod relative to the other. Rods with similar charge repel each other with a torque acting to make the rods perpendicular while rods of opposite charge attract with the parallel arrangement preferred.

Computation of van der Waals interactions in aqueous systems using reflectivity data.

Recent advances in the theory of electrodynamic interactions have made it possible to compute van der Waals forces between macroscopic bodies from spectroscopic data. Accurate data for water are available from reflection spectra in the infrared region. We show how the data can be efficiently used, as illustrated by the interaction of water across a hydrocarbon film. Hamaker coefficients are found to be in the range 3.4 to 6.8 × 10−14 erg which includes the experimental value. The theory requires evaluation of dielectric susceptibilities at imaginary frequencies. The reflection data for water give absorption frequencies, oscillator strengths, and absorption bandwidths (not available for most substances) for real (sinusoidal) frequencies. We show that the required dielectric functions and consequent computed energies are particularly insensitive to absorption bandwidths; at least in those cases where bandwidths are known, so they may be ignored in the computation of intermolecular forces. Laborious curve-fitting of dielectric susceptibilities for real frequencies so far appears unnecessary for obtaining energy estimates.