An electrostatic model with weak actin-myosin attachment resolves problems with the lattice stability of skeletal muscle

The stability of the filament lattice in relaxed striated muscle can be viewed as a balance of electrostatic and van der Waals forces. The simplest electrostatic model, where actin and myosin filaments are treated as charged cylinders, generates reasonable lattice spacings for skinned fibers. However, this model predicts excessive radial stiffness under osmotic pressure and cannot account for the initial pressure (∼1 kPa) required for significant compression. Good agreement with frog compression data is obtained with an extended model, in which S1 heads are weakly attached to actin when the lattice spacing is reduced below a critical value; further compression moves fixed negative charges on the heads closer to the myofilament backbone as they attach at a more acute angle to actin. The model predicts pH data in which the lattice shrinks as pH is lowered and protons bind to filaments. Electrostatic screening implies that the lattice shrinks with increasing ionic strength, but the observed expansion of the frog lattice at ionic strengths above 0.1 M with KCl might be explained if Cl⁻ binds to sites on the motor domain of S1. With myosin-myosin and actin-actin interactions, the predicted lattice spacing decreases slightly with sarcomere length, with a more rapid decrease when actin-myosin filament overlap is very small.     

Interactions between motile Escherichia coli and glass in media with various ionic strengths, as observed with a three-dimensional-tracking microscope.

Escherichia coli bacteria have been observed to swim along a glass surface for several minutes at a time. Settling velocities of nonmotile cells and a computer simulation of motile cells confirmed that an attractive force kept the bacteria near the surface. The goal of this study was to evaluate whether this attractive force could be explained by reversible adhesion of E. coli to the surface in the secondary energy minimum, according to the theory of Derjaguin, Landan, Verwey, and Overbeek (DLVO theory). This theory describes interactions between colloidal particles by combining attractive van der Waals forces with repulsive electrostatic forces. A three-dimensional-tracking microscope was used to follow both wild-type and smooth-swimming E. coli bacteria as they interacted with a glass coverslip in media of increasing ionic strengths, which corresponded to increasing depths of the secondary energy minimum. We found no quantifiable changes with ionic strength for either the tendencies of individual bacteria to approach the surface or the overall times bacteria spent near the surface. One change in bacterial behavior which was observed with the change in ionic strength was that the diameters of the circles which the smooth-swimming bacteria traced out on the glass increased in low-ionic-strength solution.     

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.     

Adhesion of the positively charged bacterium Stenotrophomonas (Xanthomonas) maltophilia 70401 to glass and Teflon.

Medical implants are often colonized by bacteria which may cause severe infections. The initial step in the colonization, the adhesion of bacteria to the artificial solid surface, is governed mainly by long-range van der Waals and electrostatic interactions between the solid surface and the bacterial cell. While van der Waals forces are generally attractive, the usually negative charge of bacteria and solid surfaces leads to electrostatic repulsion. We report here on the adhesion of a clinical isolate, Stenotrophomonas maltophilia 70401, which is, at physiological pH, positively charged. S. maltophilia has an electrophoretic mobility of +0.3 x 10(-8) m2 V-1 s-1 at pH 7 and an overall surface isoelectric point at pH 11. The positive charge probably originates from proteins located in the outer membrane. For this bacterium, both long-range forces involved in adhesion are attractive. Consequently, adhesion of S. maltophilia to negatively charged surfaces such as glass and Teflon is much favored compared with the negatively charged bacterium Pseudomonas putida mt2. While adhesion of negatively charged bacteria is impeded in media of low ionic strength because of a thick negatively charged diffuse layer, adhesion of S. maltophilia was particularly favored in dilute medium. The adhesion efficiencies of S. maltophilia at various ionic strengths could be explained in terms of calculated long-range interaction energies between S. maltophilia and glass or Teflon.     

Tension fluctuations in contracting myofibrils and their interpretation

Repulsive pressure has been measured as a function of lattice spacing in gels of tobacco mosaic virus (TMV) and in the filament lattice of vertebrate striated muscle. External pressures up to ten atm have been applied to these lattices by an osmotic stress method. Numerical solutions to the Poisson-Boltzmann equation in hexagonal lattices have been obtained and compared to the TMV and muscle data. The theoretical curves using values for k calculated from the ionic strength give a good fit to experimental data from TMV gels, and an approximate fit to that from the muscle lattice, provided that a charge radius for the muscle thick filaments of approximately 16 nm is assumed. Variations in ionic strength, sarcomere length and state of the muscle give results which agree qualitatively with the theory, though a good fit between experiment and theory in the muscle case will clearly require consideration of other types of forces. We conclude that Poisson-Boltzmann theory can provide a good first approximation to the long-range electrostatic forces operating in such biological gel systems.     

Direct measurements of forces between phosphatidylcholine and phosphatidylethanolamine bilayers in aqueous electrolyte solutions

We report direct measurements of the full interbilayer force laws (force vs. distance) between bilayers of various phosphatidylcholines and phosphatidylethanolamine in aqueous solutions. Bilayers were first deposited on molecularly smooth (mica) surfaces and the interbilayer forces then measured at a resolution of 1 A. Three types of forces were identified: attractive van der Waals forces, repulsive electrostatic (double-layer) forces, and (at short range) repulsive steric hydration forces. Double-layer forces, which arise from ion binding, were insignificant in monovalent salt solutions, e.g., NaCl up to 1 M, but were already present in solutions containing millimolar levels of CaCl2 and MgCl2, giving rise to forces in excellent agreement with theory. Ca2+ binds more strongly than Mg2+, and both bind less to lecithin bilayers in the fluid state (T greater than Tc). The plane of charge coincides with the location of the negative phosphate groups, while the effective plane of origin of the van der Waals force is 4-5 A farther out. In water, the adhesion energies are in the range 0.10-0.15 erg/cm2 for lecithins and approximately 0.8 erg/cm2 for phosphatidylethanolamine. The adhesion energies vary on addition of salt due to changes in the repulsive double-layer and hydration forces rather than to a change in the attractive van der Waals force. The short-range repulsive forces which balance the van der Waals force at separations of 10-30 A are due to a combination of hydration and steric repulsions, the latter arising from thermal motions of head groups and thickness fluctuations of fluid bilayers (above Tc). It is also concluded that bilayer fusion is not simply related to the interbilayer force law.     

pH control of the third virial coefficient of hyaluronate solutions calculated from van der Waals forces by means of the Lifshitz-McLachlan susceptibility theory

Positive third virial coefficients and osmotic coefficients have been calculated for human umbilical cord hyaluronic acid solutions at pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5 and constant ionic strength 0.1. The calculations are based on experimental axial flow birefringence and radial linear dichroism data previously reported and the Lifshitz-McLachlan field theory of van der Waals forces. The second virial coefficients are negative, according to both this analysis and light scattering evidence, and reflect the tendency of hyaluronic acid to associate. This negativity denies the assumption of force additivity required by virial expansion theory.The results are in reasonable agreement with those of light scattering studies, and indicate the extreme nonideality of hyaluronate solutions with a high degree of pH control of osmotic pressure. The data are explained within the context of statistical mechanical and field theories of van der Waals forces, and the osmotic pressure of a solution is related to its optical properties. The numerical method used offers a way of exploring the applicability of modern interparticle force theory to biological systems.     

The myofilament lattice: studies on isolated fibers. IV. Lattice equilibria in striated muscle.

Accounts of similarities between the thick filament lattice of striated muscle and smectic liquid-crystalline structures have focused upon an equilibrium between electrostatic (repulsive) and van der Waal's (attractive) forces. In living, intact muscle the fiber volume constitutes an additional important parameter which influences the amount of interaxial separation between the filaments. This is demonstrable by comparison of the lattice behavior of living fibers with that of fibers from which the sarcolemma has either been removed or made leaky by glycerination. These comparisons were made mainly by low-angle X-ray diffraction under conditions of changes in sarcomere length, ionic strength or osmolarity, and pH. Single fibers with the sarcolemma removed and glycerinated muscle have lattices which behave in accord with equilibrium liquid-crystalline systems in which the thick filament spacing is determined by the balance between electrostatic and van der Waal's forces. Conversely, osmotic and shortening studies demonstrate that the living, intact muscle has a lattice which behaves in accord with the so-called non-equilibrium (volume-constrained) liquid-crystalline condition in which the interaxial separation between the thick filaments is solely due to the amount of volume available as determined by the Donnan steady-state across the sarcolemma.     

Force Balances in Systems of Cylindrical Polyelectrolytes

A detailed analysis is made of the model system of two parallel cylindrical polyelectrolytes which contain ionizable groups on their surfaces and are immersed in an ionic bathing medium. The interaction between the cylinders is examined by considering the interplay between repulsive electrostatic forces and attractive forces of electrodynamic origin. The repulsive force arises from the screened coulomb interaction between the surface charge distributions on the cylinders and has been treated by developing a solution to the linearized Poisson-Boltzmann equation. The boundary condition at the cylinder surfaces is determined as a self-consistent functional of the potential, with the input consisting of the density of ionizable groups and their dissociation constants. It is suggested that a reasonably accurate representation for the form of the attractive force can be obtained by performing a pairwise summation of the individual interatomic forces. A quantitative estimate is obtained using a Hamaker constant chosen on the basis of rigorous calculations on simpler systems. It is found that a balance exists between these repulsive and attractive forces at separations in good agreement with those observed in arrays of tobacco mosaic virus and in the A band myosin lattice in striated muscle. The behavior of the balance point as a function of the pH and ionic strength of the bathing medium closely parallels that seen experimentally.     

Measuring electrostatic, van der Waals, and hydration forces in electrolyte solutions with an atomic force microscope

In atomic force microscopy, the tip experiences electrostatic, van der Waals, and hydration forces when imaging in electrolyte solution above a charged surface. To study the electrostatic interaction force vs distance, curves were recorded at different salt concentrations and pH values. This was done with tips bearing surface charges of different sign and magnitude (silicon nitride, Al₂O₃, glass, and diamond) on negatively charged surfaces (mica and glass). In addition to the van der Waals attraction, neutral and negatively charged tips experienced a repulsive force. This repulsive force depended on the salt concentration. It decayed exponentially with distance having a decay length similar to the Debye length. Typical forces were about 0.1 nN strong. With positively charged tips, purely attractive forces were observed. Comparing these results with calculations showed the electrostatic origin of this force.

In the presence of high concentrations (> 3 M) of divalent cations, where the electrostatic force can be completely ignored, another repulsive force was observed with silicon nitride tips on mica. This force decayed roughly exponentially with a decay length of 3 nm and was ~0.07-nN strong. This repulsion is attributed to the hydration force.

     

Direct measurement of the intermolecular forces between counterion-condensed DNA double helices. Evidence for long range attractive hydration forces.

Rather than acting by modifying van der Waals or electrostatic double layer interactions or by directly bridging neighboring molecules, polyvalent ligands bound to DNA double helices appear to act by reconfiguring the water between macromolecular surfaces to create attractive long range hydration forces. We have reached this conclusion by directly measuring the repulsive forces between parallel B-form DNA double helices pushed together from the separations at which they have self organized into hexagonal arrays of parallel rods. For all of the wide variety of "condensing agents" from divalent Mn to polymeric protamines, the resulting intermolecular force varies exponentially with a decay rate of 1.4-1.5 A, exactly one-half that seen previously for hydration repulsion. Such behavior qualitatively contradicts the predictions of all electrostatic double layer and van der Waals force potentials previously suggested. It fits remarkably well with the idea, developed and tested here, that multivalent counterion adsorption reorganizes the water at discrete sites complementary to unadsorbed sites on the apposing surface. The measured strength and range of these attractive forces together with their apparent specificity suggest the presence of a previously unexpected force in molecular organization.     

Electrodynamics of Lipid Membrane Interactions in the Presence of Zwitterionic Buffers

Due to thermal motion and molecular polarizability, electrical interactions in biological systems have a dynamic character. Zwitterions are dipolar molecules that typically are highly polarizable and exhibit both a positive and a negative charge depending on the pH of the solution. We use multilamellar structures of common lipids to identify and quantify the effects of zwitterionic buffers that go beyond the control of pH. We use the fact that the repeat spacing of multilamellar lipid bilayers is a sensitive and accurate indicator of the force balance between membranes. We show that common buffers can in fact charge up neutral membranes. However, this electrostatic effect is not immediately recognized because of the concomitant modification of dispersion (van der Waals) forces. We show that although surface charging can be weak, electrostatic forces are significant even at large distances because of reduced ionic screening and reduced van der Waals attraction. The zwitterionic interactions that we identify are expected to be relevant for interfacial biological processes involving lipid bilayers, and for a wide range of biomaterials, including amino acids, detergents, and pharmaceutical drugs. An appreciation of zwitterionic electrodynamic character can lead to a better understanding of molecular interactions in biological systems and in soft materials in general.     

Molecular mechanical perspective on halogen bonding

The nature and strength of halogen bonding in halo molecule-Lewis base complexes were studied in terms of molecular mechanics using our recently developed positive extra-point (PEP) approach, in which the σ-hole on the halogen atom is represented by an extra point of positive charge. The contributions of the σ-hole (i.e., positively charged extra point) and the halogen atom to the strength of this noncovalent interaction were clarified using the atomic parameter contribution to the molecular interaction (APCtMI) approach. The molecular mechanical results revealed that the halogen bond is electrostatic and van der Waals in nature, and its strength depends on three types of interaction: (1) the attractive electrostatic interaction between the σ-hole and the Lewis base, (2) the repulsive electrostatic interaction between the negative halogen atom and the Lewis base, and (3) the repulsive/attractive van der Waals interactions between the halogen atom and the Lewis base. The strength of the halogen bond increases with increasing σ-hole size (i.e., magnitude of the extra-point charge) and increasing halogen atom size. The van der Waals interaction's contribution to the halogen bond strength is most favorable in chloro complexes, whereas the electrostatic interaction is dominant in iodo complexes. The idea that the chloromethane molecule can form a halogen bond with a Lewis base was revisited in terms of quantum mechanics and molecular mechanics. Although chloromethane does produce a positive region along the C-Cl axis, basis set superposition error corrected second-order M?ller-Plesset calculations showed that chloromethane-Lewis base complexes are unstable, producing halogen-Lewis base contacts longer than the sum of the van der Waals radii of the halogen and O/N atoms. Molecular mechanics using the APCtMI approach showed that electrostatic interactions between chloromethane and a Lewis base are unfavorable owing to the high negative charge on the chlorine atom, which overcomes the corresponding favorable van der Waals interactions.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.     

Protein interactions in the calf eye lens: interactions between β-crystallins are repulsive whereas in γ-crystallins they are attractive

Non-specific interactions in beta- and gamma-crystallins have been studied by solution X-ray scattering and osmotic pressure experiments. Measurements were carried out as a function of protein concentration at two ionic strengths. The effect of temperature was tested between 7 degrees C and 31 degrees C. Two types of interactions were observed. With beta-crystallin solutions, a repulsive coulombic interaction could be inferred from the decrease of the normalized X-ray scattering intensity near the origin with increasing protein concentration and from the fact that the osmotic pressure increases much more rapidly than in the ideal case. As was previously observed with alpha-crystallins, such behaviour is dependent upon ionic strength but is hardly affected by temperature. In contrast, with gamma-crystallin solutions, the normalized X-ray scattering intensity near the origin increases with increasing protein concentration and the osmotic pressure increases less rapidly than in the ideal case. Such behaviour indicates that attractive forces are predominant, although we do not yet know their molecular origin. Under our experimental conditions, the effect of temperature was striking whereas no obvious contribution of the ionic strength could be seen, perhaps owing to masking by the large temperature effect. The relevance of the different types of non-specific interactions for lens function is discussed.     

Morphology of modified regenerated model cellulose II surfaces studied by atomic force microscopy: effect of carboxymethylation and heat treatment

Model cellulose II surfaces with different surface charge have been prepared from carboxymethylated wood pulp. AFM tapping-mode imaging in air showed that the introduction of charged groups into the film does not appreciably change the surface morphology. However, after a mild heat treatment (heating at 105 degrees C for 6 h), an irreversible surface structure change, from near spherical-type aggregates to a fibrillar structure, was observed. This might be attributed to the formation of strong hydrogen bonds in the crystalline region of the films while the amorphous regions shrank upon drying. The suitability of these charged cellulose films for surface forces studies was also investigated. At pH below the pK(a) of the carboxyl groups present in the film, the interaction force could be fit by a van der Waals force interaction. At higher pH, the interaction was of a purely electrostatic nature with no van der Waals component observable due to the swelling of the surfaces.     

The osmotic pressure of chondroitin sulphate solutions: experimental measurements and theoretical analysis

We used equilibrium dialysis to measure the osmotic pressure of chondroitin sulphate (CS) solutions as a function of their concentration and fixed charge density (FCD) and the ionic strength and composition of the solution. Osmotic pressure varied nonlinearly with the concentration of chondroitin sulphate and in 0.15 M NaCl at FCDs typical of uncompressed cartilage (approximately 0.4 mmol/g extrafibrillar H2O) was approximately 3 atmospheres. Osmotic pressure fell by 60% as solution ionic strength increased up to about 1 M, but remained relatively constant at higher ionic strengths. The ratio of Ca2+ to Na+ in the medium was a minor determinant of osmotic pressure. The data are compared with a theoretical model of the electrostatic contribution to osmotic pressure calculated from the Poisson-Boltzmann equation using a rod-in-cell model for CS. The effective radius of the polyelectrolyte rod is taken as a free parameter. The model qualitatively reproduces the non-linear concentration dependence, but underestimates the osmotic pressure by an amount that is independent of ionic strength. This difference, presumably arising from oncotic and entropic effects, is approximately 1/3 of the total osmotic pressure at physiological polymer concentrations and ionic strength.     

The stacking of chloroplast thylakoids: Quantitative analysis of the balance of forces between thylakoid membranes of chloroplasts,and the role of divalent cations

An analysis is made of the van der Waals dispersion attractive forces and electrostatic repulsive forces between the grana thylakoid membranes of chloroplasts. These forces are determined for negatively charged surfaces with a pK_a value of 4.7 for a bulk pH of 7.0 with a range of mono- and divalent cation concentrations and intermembrane spacing in the range 10 to 80 Å. For equilibrium under dark conditions, it is concluded that either there is extensive electrostatic binding of divalent cations (Mg²⁺) to the negatively charged membrane groups (phospholipid, sulfolipid, and protein carboxyl), or a redistribution of these groups between stacked and unstacked regions must be invoked.     

Two-phase formation in solutions of tobacco mosaic virus and the problem of long-range forces

In a nearly salt-free medium, a dilute tobacco mosaic virus solution of rod-shaped virus particles of uniform length forms two phases; the bottom optically anisotropic phase has a greater virus concentration than has the top optically isotropic phase. For a sample containing particles of various lengths, the bottom phase contains longer particles than does the top and the concentrations top and bottom are nearly equal. The longer the particles the less the minimum concentration necessary for two-phase formation. Increasing the salt concentration increases the minimum concentration. The formation of two phases is explained in terms of geometrical considerations without recourse to the concept of long-range attractive forces. The minimum concentration for two-phase formation is that concentration at which correlation in orientation between the rod-shaped particles begins to take place. This concentration is determined by the thermodynamically effective size and shape of the particles as obtained from the concentration dependence of the osmotic pressure of the solutions measured by light scattering. The effective volume of the particles is introduced into the theory of Onsager for correlation of orientation of uniform size rods and good agreement with experiment is obtained. The theory is extended to a mixture of non-uniform size rods and to the case in which the salt concentration is varied, and agreement with experiment is obtained. The thermodynamically effective volume of the particles and its dependence on salt concentration are explained in terms of the shape of the particles and the electrostatic repulsion between them. Current theories of the hydration of proteins and of long-range forces are critically discussed. The bottom layer of freshly purified tobacco mosaic virus samples shows Bragg diffraction of visible light. The diffraction data indicate that the virus particles in solution form three-dimensional crystals approximately the size of crystalline inclusion bodies found in the cells of plants suffering from the disease.     

Osmotic pressure and packaging structure of caged DNA

We present a theoretical model for aqueous solutions of double-stranded (ds) DNA with explicit consideration of electrostatic interactions, excluded-volume effects, van der Waals attractions, and salt ions. With reasonable parameters estimated from the DNA structure and experimental data for electrolytes, we are able to reproduce the DNA osmotic pressure in the bulk in good agreement with experiment. The predicted DNA osmotic pressure in λ-bacteriophages is found to coincide with that of the PEG8000 solution that inhibits DNA ejection as reported in recent experiments. Based on the radial distributions of DNA segments and of counterions at different degrees of packaging, we find that in the presence of Mg²⁺, DNA forms a multilayer structure near the inner surface of a fully loaded bacteriophage, but at low packing density the DNA segments are depleted from the surface owing to the local condensation of DNA induced by the divalent counterions. By contrast, the multilayer DNA structure is less distinctive in the presence of Na⁺ despite the increase of the DNA density at contact, and the depletion near the capsid surface is not found at low packing density.