Interrod forces in aqueous gels of tobacco mosaic virus.

The lateral separation of virus rod particles of tobacco mosaic virus has been studied as a function of externally applied osmotic pressure using an osmotic stress technique. The results have been used to test the assumption that lattice equilibrium in such gels results from a balance between repulsive (electrostatic) and attractive (van der Waals and osmotic) forces. Results have been obtained at different ionic strengths (0.001 to 1.0 M) and pH's (5.0 to 7.2) and compared with calculated curves for electrostatic nad van der Waals pressure. Under all conditions studied, interrod spacing decreased with increasing applied pressure, the spacings being smaller at higher ionic strengths. Only small differences were seen when the pH was changed. At ionic strengths near 0.1 M, agreement between theory and experiment is good, but the theory appears to underestimate electrostatic forces at high ionic strengths and to underestimate attractive forces at large interrod spacings (low ionic strengths). It is concluded that an electrostatic-van der Waals force balance can explain stability in tobacco mosaic virus gels near physiological conditions and can provide a good first approximation elsewhere.     

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.     

Lateral forces in the filament lattice of vertebrate striated muscle in the rigor state.

The repulsive pressure between filaments in the lattice of skinned rabbit and frog striated muscle in rigor has been measured as a function of interfilament spacing, using the osmotic pressure generated by solutions of large, uncharged polymeric molecules (dextran and polyvinylpyrrolidone). The pressure/spacing measurements have been compared with theoretically derived curves for electrostatic pressure. In both muscles, the major part of the experimental curves (100-2,000 torr) lies in the same region as the electrostatic pressure curves, providing that a thick filament charge diameter of approximately 30 nm in rabbit and approximately 26 nm in frog is assumed. In chemically skinned or glycerol-extracted rabbit muscle the fit is good; in chemically skinned frog sartorius and semitendinosus muscle the fit is poor, particularly at lower pressures where a greater spacing is observed than expected on theoretical grounds. The charge diameter is much larger than the generally accepted value for thick filament backbone diameter. This may be because electron microscope results have underestimated the amount of filament shrinkage during sample preparation, or because most of the filament charge is located at some distance from the backbone surface, e.g., on HMM-S2. Decreasing the ionic strength of the external solution, changing the pH, and varying the sarcomere length all give pressure/spacing changes similar to those expected from electrostatic pressure calculations. We conclude that over most of the external pressure range studied, repulsive pressure in the lattice is predominantly electrostatic.     

Calculation of the Electrophoretic Mobility of a Particle Bearing Bound Polyelectrolyte Using the Nonlinear Poisson-Boltzmann Equation

A numerical method for determining the electrophoretic mobility of a polyelectrolyte-coated particle is presented. The particle surface is modeled as having a permeable layer of polyelectrolyte molecules anchored to its surface. Fluid flow within the polyelectrolyte layer is subject to Stokes drag arising from the polyelectrolyte segments. The method allows arbitrary distribution of polymer segments and charge density normal to the surface to be used. The hydrodynamic plane of shear may also be varied. The potential profile is determined by a numerical solution to the nonlinearized Poisson-Boltzmann equation. The potential profile is then used in a numerical solution to the Navier-Stokes equation to give the required mobility. The use of the nonlinearized Poisson-Boltzmann equation extends the results to higher charge density/lower ionic strength conditions than previous treatments. The surface potentials and mobilities for three limiting charge distributions are compared for both the linear and nonlinear treatments to delimit the range of validity of the linear treatment. The utility of the numerical, nonlinear treatment is demonstrated by an improved fit to the electrophoretic mobility of human erythrocytes as a function of ionic strength in the range 10 to 150 mM.     

Average electrostatic potential between the filaments in striated muscle and its relation to a simple Donnan potential.

An approximate analytical solution to the Poisson-Boltzmann equation for a cylindrical particle was used to calculate the relationship between the charge on the filaments and the average electrostatic potential. Both thick and then filaments were considered in the muscle lattice with a filament charge ratio of 4 to 1. Comparing this with a similar relationship obtained using simple Donnan theory showed a discrepancy at high charge where the Poisson-Boltzmann equation leads to saturation of the average potential. However, using two separate experiments from the literature, we have shown that at pH 7.0 muscle must not be close to saturation and thus is in a region of the curve where the two approaches agree.     

Mechanical behavior of fibroblasts included in collagen lattices

Striae distensae are characterized by linear, smooth bands of atrophic-appearing skin. Excessive steroid activity, genetic and mechanical factors and inherited defects of connective tissues are the most frequent causes of this disease. Fibroblasts derived from women presenting striae distensae lesions were included into collagen gels to study their mechanical behavior: capacity to contract free-floating lattices and to produce isometric force in tense lattices. To measure the retracted lattice diameter, the culture dishes were placed on a transparent metric scale. An isometric force system was used to study quantitatively the forces developed during lattice contraction. alpha 2 beta 1 integrins expression (transmembrane receptors) was evaluated by flux cytometry. Striae distensae fibroblasts contract collagen gels slower than normal human fibroblasts but the final contraction is similar. They produce a greater isometric force which is associated with enhanced alpha 2 beta 1 integrins expression. By their mechanical properties, striae distensae fibroblasts appear as a different population from normal fibroblasts.     

Application of polyelectrolyte theory to the study of the B-Z transition in DNA (1)

We have used the polyelectrolyte theory to study the ionic strength dependence of the B-Z equilibrium in DNA. A DNA molecule is molded as an infinitely long continuously charged cylinder of radius a with reduced linear charge density q. The parameters a and q for the B and Z forms were taken from X-ray data: aB = 1nm, qB = 4.2, aZ = 0.9 nm and qZ = 3.9. A simple theory shows that at low ionic strengths (when Debye screening length rD much greater than a) the electrostatic free energy difference FelBZ = FelZ - FelB increases with increasing ionic strength since qB greater than qZ. At high ionic strengths (when rD much less than a) the FelBZ would go on growing with increasing ionic strength if the inequality qB/aB greater than qZ/aZ were valid. In the converse case when qZ/qB greater than aZ/aB the FelBZ value decreases with increasing salt concentration at high ionic strength. Since X-ray data correspond to the latter case, theory predicts that the FelBZ value reaches a maximum at an intermediate ionic strength of about 0.1 M (where rD approximately a). We also performed rigorous calculations based on the Poisson-Boltzmann equation. These calculations have confirmed the above criterion of nonmonotonous behaviour of the FelBZ value as a function of ionic strength. Different theoretical predictions for the B-Z transition in linear and superhelical molecules are discussed. Theory predicts specifically that at a very low ionic strength the Z form may prove to be more stable than the B form.(ABSTRACT TRUNCATED AT 250 WORDS)     

Interaction of tobacco mosaic virus and tobacco mosaic virus protein with bovine serum albumin.

Bovine serum albumin (BSA) causes tobacco mosaic virus (TMV) to crystallize at pH values where both have negative charges. The amount of albumin required to precipitate the virus varies inversely with ionic strength of added electrolyte. At pH values above 5, the precipitating power is greatest when BSA has the maximum total, positive plus negative, charge. Unlike early stages of the crystallization of TMV in ammonium sulfate-phosphate solutions, which can be reversed by lowering the temperature, the precipitation of TMV by BSA is not readily reversed by changes in temperature. The logarithm of the apparent solubility of TMV in BSA solutions, at constant ionic strength of added electrolyte, decreases linearly with increasing BSA concentration. This result and the correlation of precipitating power with total BSA charge suggest that BSA acts in the manner of a salting-out agent. The effect of BSA on the reversible entropy-driven polymerization of TMV protein (TMVP) depends on BSA concentration, pH, and ionic strength. In general, BSA promotes TMVP polymerization, and this effect increases with increasing BSA concentrations. The effect is larger at pH 6.5 than at pH 6. Even though increasing ionic strength promotes polymerization of TMVP in absence of BSA, the effect of increasing ionic strength from 0.08 to 0.18 at pH 6.5 decreases the polymerization-promoting effect of BSA. Likewise, the presence of BSA decreases the polymerization-promoting effect of ionic strength. The polymerization-promoting effect of BSA can be interpreted in terms of a process akin to salting-out. The mutual suppression of the polymerization-promoting effects of BSA and of electrolytes by each other can be partially explained in terms of salting-in of BSA.     

The Donnan effect in tobacco mosaic virus and its components

Osmotic pressure studies were carried on tobacco mosaic virus (TMV) and its components, protein and RNA, as well as on bis(3,3′-aminopropyl)amine, reported to be present in TMV preparations. Solvents were phosphate and barbital buffers at different values of pH and ionic strength. Measurements were made at room temperature. The Donnan effect was exhibited by TMV protein in phosphate buffer of 0.01 ionic strength at pH values ranging between 5.8 and 7.5. The observed values of the Donnan effect at pH 5.8 and 5.97 were in reasonable agreement with theoretical values calculated from the charge obtained by hydrogen ion titration. TMV-RNA in phosphate buffer at pH 7.5 and ionic strength 0.01 did not exhibit more than 1% of the expected Donnan effect. This is explained tentatively as the result of firm binding of metal ions. Negative values of osmotic pressure were observed with bis(3,3′-aminopropyl)amine. Similar anomalous osmosis was sometimes observed with TMV protein and with TMV. In agreement with earlier observations, TMV did not exhibit the Donnan effect in phosphate buffer of 0.01 ionic strength at pH values ranging from 5.5 to 8.0. However, TMV dialysed extensively in the presence of EDTA at pH 8.5 and TMV produced by reconstitution of purified protein and RNA did exhibit the Donnan effect in both phosphate and barbital buffers. The magnitude was of the same order as that calculated from the net charge determined by hydrogen ion titration. When reconstituted TMV, which did exhibit Donnan effect, was treated with calcium ions, the effect was abolished.     

Ionic strength dependence of F-actin and glycolytic enzyme associations: a Brownian dynamics simulations approach

The association of glycolytic enzymes with F-actin is proposed to be one mechanism by which these enzymes are compartmentalized, and, as a result, may possibly play important roles for: regulation of the glycolytic pathway, potential substrate channeling, and increasing glycolytic flux. Historically, in vitro experiments have shown that many enzyme/actin interactions are dependent on ionic strength. Herein, Brownian dynamics (BD) examines how ionic strength impacts the energetics of the association of F-actin with the glycolytic enzymes: lactate dehydrogenase (LDH), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), fructose-1,6-bisphosphate aldolase (aldolase), and triose phosphate isomerase (TPI). The BD simulations are steered by electrostatics calculated by Poisson-Boltzmann theory. The BD results confirm experimental observations that the degree of association diminishes as ionic strength increases but also suggest that these interactions are significant, at physiological ionic strengths. Furthermore, BD agrees with experiments that muscle LDH, aldolase, and GAPDH interact significantly with F-actin whereas TPI does not. BD indicates similarities in binding regions for aldolase and LDH among the different species investigated. Furthermore, the residues responsible for salt bridge formation in stable complexes persist as ionic strength increases. This suggests the importance of the residues determined for these binary complexes and specificity of the interactions. That these interactions are conserved across species, and there appears to be a general trend among the enzymes, support the importance of these enzyme-F-actin interactions in creating initial complexes critical for compartmentation.     

X-ray diffraction testing for weak-binding crossbridges in relaxed bony fish muscle fibres at low ionic strength

Equatorial X-ray diffraction patterns from single skinned fibres from bony fish muscle (turbot) were obtained with the fibres at 6 degrees C bathed in relaxing solutions of 170 down to 26 mM ionic strength. Diffraction patterns from rigor fibres were also obtained as controls. Unlike fibres from rabbit muscle, which show very clear evidence of substantial crossbridge formation at low ionic strength in what is mechanically a rapid equilibrium ("weak-binding") state (Brenner et al., 1982), diffraction patterns from bony fish fibres showed only a small change in relative peak intensities at low ionic strength (26 mM) compared with normal (170 mM) ionic strength. However, there was a slight ordering of the filament lattice at low ionic strength. The specimen temperature used (about 6 degrees C) was not far from the normal physiological temperature of the fish. Likewise, only a small change was seen by Xu et al. (1987) in patterns from frog fibres at low ionic strength at 2 to 6 degrees C. (Rabbit fibres previously studied, where large changes were seen at temperatures of 5 to 20 degrees C, were about 17 to 32 degrees C below physiological.) The I11/I10 ratio for fish fibres at 26 mM ionic strength was actually lower than that for rabbit even at normal ionic strength. This may be associated with an intrinsic structural difference between these muscles or alternatively with the disordering of the crossbridge helix in rabbit muscle found at low temperature by Wray (1987), and could support the view that rabbit fibres at 5 degrees C and normal ionic strength may already have a significant population of weak-binding crossbridges.     

Chromatin ionic atmosphere analyzed by a mesoscale electrostatic approach

Characterizing the ionic distribution around chromatin is important for understanding the electrostatic forces governing chromatin structure and function. Here we develop an electrostatic model to handle multivalent ions and compute the ionic distribution around a mesoscale chromatin model as a function of conformation, number of nucleosome cores, and ionic strength and species using Poisson-Boltzmann theory. This approach enables us to visualize and measure the complex patterns of counterion condensation around chromatin by examining ionic densities, free energies, shielding charges, and correlations of shielding charges around the nucleosome core and various oligonucleosome conformations. We show that: counterions, especially divalent cations, predominantly condense around the nucleosomal and linker DNA, unburied regions of histone tails, and exposed chromatin surfaces; ionic screening is sensitively influenced by local and global conformations, with a wide ranging net nucleosome core screening charge (56-100e); and screening charge correlations reveal conformational flexibility and interactions among chromatin subunits, especially between the histone tails and parental nucleosome cores. These results provide complementary and detailed views of ionic effects on chromatin structure for modest computational resources. The electrostatic model developed here is applicable to other coarse-grained macromolecular complexes.     

Ion transport through thin lipid films

Currents through thin lipid films were measured versus temperature, applied voltage, pH value, ionic strength and ionic species. All experimental data tend to fit a two-component current theory, that is, the film current composed of a surface barrier jumping current and a surface recombination current. A good agreement was obtained in surface barrier height between theory and experiment. Breakdown phenomenon was observed and is interpreted as possibly arising from avalanche multiplication of ions, most probably from surface traps.     

Structure and function of disk aggregates of the coat protein of tobacco mosaic virus

Experiments have been carried out on the coat protein of tobacco mosaic virus (TMVP) to test for the occurrence of the previously postulated RNA-induced direct switching, during in vitro assembly of tobacco mosaic virus (TMV), of the subunit packing from the cylindrical bilayer disk to the virus helical arrangement. No evidence was found for such RNA-induced switching and no evidence for the direct participation of the bilayer disk in either the nucleation or elongation phases of the in vitro virus assembly. Instead, virus assembly proceeds by an initiation step involving the binding of the RNA to the previously characterized two-plus turn helical aggregate that is formed from small oligomers of subunits. However, a bilayer disk, which has been characterized in high ionic strength crystals, has been observed in low ionic strength virus assembly solutions only as a transient species upon depolymerization of dimers of bilayer disks formed in solution at high ionic strength, and not as an equilibrium species of TMVP.     

Simulation of electrostatic effects in Fab-antigen complex formation.

A model based on the Poisson-Boltzmann equation has been used to model electrostatics in Anti-p24 (HIV-1) Fab-antigen association. The ionization state at different pH values has been simulated and the results have been used to estimate the stability at different pH values and to generate electrostatic potential maps at physiological ionic strength. The analysis of the electrostatic potential at the solvent-accessible surface shows that residues involved in binding are mostly found in the highest, but also in lowest potential regions. Brownian dynamics simulations have been used to estimate the enhancement of the association rate due to electrostatics which appears limited (approximately 2 at 150 mM ionic strength and approximately 3 at 15 mM ionic strength). A much more pronounced effect is observed upon increase of the charge of the diffusing particle. These results compare well with results obtained previously in similar studies on different systems and may serve to estimate the expected order of magnitude of electrostatic effects on association rates in antibody-antigen systems.     

Cyclic AMP-induced inhibition of collagen lattice contraction by fibroblasts may be attenuated by both cyclic AMP dependent and independent mechanisms

The contraction of collagen lattices made with forskin fibroblasts in medium containing 1% fetal bovine serum was inhibited by intracelluar cyclic AMP raising drugs including cholera toxin (CT), forskolin, and dibutyryl-cAMP. The inhibition by CT was attenuated by insulin, acidic fibroblast growth factor (aFGF), and transforming growth factor-β (TGF-β). All three peptide factors have previously been reported to promote collagen lattice contraction by arterial smooth muscle cells and/or fibroblasts. Incubation of cells suspended in collagen gels with CT and forskolin resulted in a transient rise of the intracellular cyclic AMP levels, which peaked at 2 hr and 30 min, respectively, after drug exposure. Cholera toxin-induced intracellular cyclic AMP increase was attenuated by TGF-β, but not by aFGF and insulin, when added simultaneously. Thus, TGF-β may attenuate CT's inhibition on collagen lattice contraction by attenuating CTinduced intracellualr cyclic AMP increse, whereas the attenuation by insulin and aFGF on the inhibition of lattice contraction may be mediated by a cyclic AMPindependent mechannism. © 1993 Wiley-Liss, Inc.     

Influence of the ionic strength on the heat-induced aggregation of the globular protein beta-lactoglobulin at pH 7

The influence of the ionic strength on the structure of beta-lactoglobulin aggregates formed after heating at pH 7 has been studied using static and dynamic light scattering. The native protein depletion has been monitored using size exclusion chromatography. Above a critical association concentration (CAC) well-defined clusters are formed containing about 100 monomers. The CAC increases with decreasing ionic strength. The so-called primary aggregates associate to form self similar semi-flexible aggregates with a large scale structure that is only weakly dependent on the ionic strength. The local density of the aggregates increases with increasing ionic strength. At a critical gel concentration, Cg, the size of the aggregates diverges. Cg decreases from 100 g/l without added salt to 1 g/l at 0.4M NaCl. For C > Cg the system gels except at high ionic strength close to Cg where the gels collapse under gravity and a precipitate is formed.     

Ordered association of tobacco mosaic virus in the presence of divalent metal ions

The formation of ordered aggregates of tobacco mosaic virus (TMV) in the presence of divalent metal ions has been studied in concentrated (1-25 mg/ml) solutions of the virus. The divalent metal cations Cd2+, Zn2+, Pb2+, Cu2+, and Ni2+ have been found to promote TMV precipitation from solution at a critical concentration Ccrit, which for a given metal depends on the pH and the ionic strength of the solution, but is largely independent of the virus concentration. The TMV precipitate behaves as a nematic liquid crystal and on drying at a glass surface produces highly ordered, optically birefringent films. However, precipitation is not observed with alkali-earth metals such as Ca2+ and Mg2+. The experimental data suggest that, apart from two 'internal' metal-binding sites in each TMV subunit, the virus contains metal-binding sites of a lower affinity which promote cross-linking of TMV rods via metal bridges. The latter seem to be responsible for the precipitation of TMV in the presence of divalent cations at neutral pH. We propose that the metal-induced cross-linking may be the predominant mechanism to account for the limited solubility of a variety of proteins in solution containing metal cations with valence 2 and higher.     

A method of quantification of stress shielding in the proximal femur using hierarchical computational modeling

Stress shielding is a biomechanical phenomenon causing adaptive changes in bone strength and stiffness around metallic implants, which potentially lead to implant loosening. Accordingly, there is a need for standard, objective engineering measures of the "stress shielding" performances of an implant that can be employed in the process of computer-aided implant design. To provide and test such measures, we developed hierarchical computational models of adaptation of the trabecular microarchitecture at different sites in the proximal femur, in response to insertion of orthopaedic screws and in response to hypothetical reductions in hip joint and gluteal muscle forces. By identifying similar bone adaptation outcomes from the two scenarios, we were able to quantify the stress shielding caused by screws in terms of analogous hypothetical reductions in hip joint and gluteal muscle forces. Specifically, we developed planar lattice models of trabecular microstructures at five regions of interest (ROI) in the proximal femur. The homeostatic and abnormal loading conditions for the lattices were determined from a finite element model of the femur at the continuum scale and fed to an iterative algorithm simulating the adaptation of each lattice to these loads. When screws were inserted to the femur model, maximal simulated bone loss (17% decrease in apparent density, 10% decrease in thickness of trabeculae) was at the greater trochanter and this effect was equivalent to the effect of 50% reduction in gluteal force and normal hip joint force. We conclude that stress shielding performances can be quantified for different screw designs using model-predicted hypothetical musculoskeletal load fractions that would cause a similar pattern and extent of bone loss to that caused by the implants.