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 Å 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 Å characteristic decay length for intermolecular attractions between condensed DNA molecules.     

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.     

Conformational Activation of Antithrombin by Heparin Involves an Altered Exosite Interaction with Protease

Heparin allosterically activates antithrombin as an inhibitor of factors Xa and IXa by enhancing the initial Michaelis complex interaction of inhibitor with protease through exosites. Here, we investigate the mechanism of this enhancement by analyzing the effects of alanine mutations of six putative antithrombin exosite residues and three complementary protease exosite residues on antithrombin reactivity with these proteases in unactivated and heparin-activated states. Mutations of antithrombin Tyr²⁵³ and His³¹⁹ exosite residues produced massive 10–200-fold losses in reactivity with factors Xa and IXa in both unactivated and heparin-activated states, indicating that these residues made critical attractive interactions with protease independent of heparin activation. By contrast, mutations of Asn²³³, Arg²³⁵, Glu²³⁷, and Glu²⁵⁵ exosite residues showed that these residues made both repulsive and attractive interactions with protease that depended on the activation state and whether the critical Tyr²⁵³/His³¹⁹ residues were mutated. Mutation of factor Xa Arg¹⁴³, Lys¹⁴⁸, and Arg¹⁵⁰ residues that interact with the exosite in the x-ray structure of the Michaelis complex confirmed the importance of all residues for heparin-activated antithrombin reactivity and Arg¹⁵⁰ for native serpin reactivity. These results demonstrate that the exosite is a key determinant of antithrombin reactivity with factors Xa and IXa in the native as well as the heparin-activated state and support a new model of allosteric activation we recently proposed in which a balance between attractive and repulsive exosite interactions in the native state is shifted to favor the attractive interactions in the activated state through core conformational changes induced by heparin binding.     

Parametrization of direct and soft steric-undulatory forces between DNA double helical polyelectrolytes in solutions of several different anions and cations.

Directly measured forces between DNA helices in ordered arrays have been reduced to simple force coefficients and mathematical expressions for the interactions between pairs of molecules. The tabulated force parameters and mathematical expressions can be applied to parallel molecules or, by transformation, to skewed molecules of variable separation and mutual angle. This "toolbox" of intermolecular forces is intended for use in modelling molecular interactions, assembly, and conformation. The coefficients characterizing both the exponential hydration and the electrostatic interactions depend strongly on the univalent counterion species in solution, but are only weakly sensitive to anion type and temperature (from 5 to 50 degrees C). Interaction coefficients for the exponentially varying hydration force seen at spacings less than 10 to 15 A between surfaces are extracted directly from pressure versus interaxial distance curves. Electrostatic interactions are only observed at larger spacings and are always coupled with configurational fluctuation forces that result in observed exponential decay lengths that are twice the expected Debye-Huckel length. The extraction of electrostatic force parameters relies on a theoretical expression describing steric forces of molecules "colliding" through soft exponentially varying direct interactions.     

Theoretical studies on protein-nucleic acid interactions. I. Interaction of positively charged amino acids with nucleic acid fragments

Coulombic interactions between the side chains of charged amino acids (Arg⁺, Lys⁺, and His⁺) and negatively charged phosphate groups of nucleic acid fragments have been studied theoretically. Diribose monophosphate and dideoxyribose monophosphate are chosen as model systems for single-stranded RNA and DNA, respectively. The interaction energies have been calculated by second-order perturbation theory using simplified formulas for individual terms. The interaction energy in this formalism is a sum of electrostatic, polarization, dispersion, and repulsive energies. Our results show that about 90% of the total interaction energy is contributed by the electrostatic term alone. Contribution from the repulsive term exceeds that from the dispersion term. Calculated interaction energies suggest that Lys⁺ and His⁺ form more stable complexes with RNA than with single-stranded DNA. On the other hand, Arg⁺ has a higher affinity for DNA than for RNA. The affinity of nucleic acids for the three amino acids is in the order Lys⁺ > His⁺ > Arg⁺. Further, the basic amino acid residues form more stable complexes with A-DNA than with B-DNA. The role of the Coulombic interactions in the specific recognition of nucleic acids by proteins is discussed.     

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.     

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.     

Direct measurement of temperature-dependent solvation forces between DNA double helices.

The assembly of double stranded DNA helices with divalent manganese ion is favored by increasing temperature. Direct force measurements, obtained from the osmotic stress technique coupled with x-ray diffraction, show that the force characteristics of spontaneously precipitated Mn(2+)-DNA closely resemble those observed previously by us for other counterion condensed DNA assemblies. At temperatures below the critical one for spontaneous assembly, we have quantitated the changes in entropy and manganese ion binding associated with the transition from repulsive to attractive interactions between helices mediated by osmotic stress. The release of structured water surrounding the DNA helix to the bulk solution is the most probable source of increased entropy after assembly. Increasing the water entropy of the bulk solution by changing the manganese salt anion from CI- to ClO4- predictably and quantitatively increases the transition entropy. This is further evidence for the dominating role of water in the close interaction of polar surfaces.     

Exclusion of alcohols from spermidine-DNA assemblies: probing the physical basis of preferential hydration

The interaction of the alcohols 2-methyl-2,4-pentanediol (MPD) and 2-propanol and of glycerol with condensed spermidine(3+)-DNA arrays are investigated with direct force measurements using osmotic stress coupled with X-ray scattering. Thermodynamic forces between DNA helices are measured from the dependence of helical interaxial spacings on the osmotic pressure applied by poly(ethylene glycol) solutions in equilibrium with the DNA phase. The sensitivity of these forces to solute concentration can be transformed into a change in the number of excess or deficit solutes or waters in the DNA phase by applying the Gibbs-Duhem equation. The alcohols examined are excluded from the condensed DNA array and strongly affect the osmotic stress force curves. DNA is preferentially hydrated. MPD is significantly more excluded than 2-propanol. The exclusion of these alcohols, however, is not due to a steric repulsion since glycerol that is intermediate in size between MPD and 2-propanol does not observably affect DNA force curves. As the distance between DNA helices varies, the change in the number of excess waters is independent of alcohol concentration for each alcohol. These solutes are acting osmotically on the condensed array. The distance dependence of exclusion indicates that repulsive water structuring forces dominate the interaction of alcohols with the DNA surface. The exclusion measured for these condensed arrays can quantitatively account for the effect of these alcohols on the precipitation of DNA from dilute solution by spermidine(3+).     

Why forces between proteins follow different Hofmeister series for pH above and below pI

The relative effectiveness of different anions in crystallizing proteins follows a reversed Hofmeister sequence for pHpI. The phenomenon has been known almost since Hofmeister's original work but it has not been understood. It is here given a theoretical explanation. Classical electrolyte and double layer theory deals only with electrostatic forces acting between ions and proteins. Hydration and hydration interactions are dealt with usually only in terms of assumed hard core models. But there are, at and above biological salt concentrations, other non-electrostatic (NES) ion-specific forces acting that are ignored in such modeling. Such electrodynamic fluctuation forces are also responsible for ion-specific hydration. These missing forces are variously comprehended under familiar but generally unquantified terms, typically, hydration, hydrogen bonding, pi-electron-cation interactions, dipole-dipole, dipole-induced dipole and induced dipole-induced dipole forces and so on. The many important body electrodynamic fluctuation force contributions are accessible from extensions of Lifshitz theory from which, with relevant dielectric susceptibility data on solutions as a function of frequency, the forces can be extracted quantitatively, at least in principle. The classical theories of colloid science that miss such contributions do not account for a whole variety of ion-specific phenomena. Numerical results that include these non-electrostatic forces are given here for model calculations of the force between two model charge-regulated hen-egg-white protein surfaces. The surfaces are chosen to carry the same charge groups and charge density as the protein. What emerges is that for pHpI (where anions are co-ions) the forces increase in the order NaCl相似文献   

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.

     

A molecular dynamics simulation study of the effect of water–graphene interaction on the properties of confined water

The role of water in determining the structure and stability of biomacromolecules has been well studied. In this work, molecular dynamics simulations have been applied to investigate the effect of surface hydrophobicity on the structure and dynamics of water confined between graphene surfaces. In order to evaluate this effect, we apply various attractive/repulsive water–graphene interaction potentials (hydrophobicity). The properties of confined water are studied by applying a purely repulsive interaction potential between water–graphene (modelled as a repulsive r^?12 potential) and repulsive–attractive forces (modelled as an LJ(12-6) potential). Compared to the case of a purely repulsive graphene–water potential, the inclusion of repulsive–attractive forces leads to formation of sharp peaks for density and the number of hydrogen bonds. Also, it was found that repulsive–attractive graphene–water potential caused slower hydrogen bonds dynamics and restricted the diffusion coefficient of water. Consequently, it was found that hydrogen bond breakage and formation rate with the repulsive r^?12 potential model, will increase compared to the corresponding water confined with the LJ(12-6) potential.     

Formation of ordered domains in membrane-bound DNA.

The interactions between DNA molecules adsorbed on fluid membranes are calculated. The adsorbing DNA perturbs the equilibrium packing of the lipids, thereby giving rise to membrane-induced, attractive interactions. These balance the direct repulsive interactions between DNA molecules. As a result, DNA adsorbed on membranes is predicted to form ordered domains characterized by a finite spacing, which varies with the membrane characteristics and the solution Debye screening length. Comparing the model predictions to recent experiments (Yang et al. 1996) yields excellent agreement with only one free (i.e., experimentally unknown) parameter.     

Spatial extent of charge repulsion regulates assembly pathways for lysozyme amyloid fibrils

Formation of large protein fibrils with a characteristic cross β-sheet architecture is the key indicator for a wide variety of systemic and neurodegenerative amyloid diseases. Recent experiments have strongly implicated oligomeric intermediates, transiently formed during fibril assembly, as critical contributors to cellular toxicity in amyloid diseases. At the same time, amyloid fibril assembly can proceed along different assembly pathways that might or might not involve such oligomeric intermediates. Elucidating the mechanisms that determine whether fibril formation proceeds along non-oligomeric or oligomeric pathways, therefore, is important not just for understanding amyloid fibril assembly at the molecular level but also for developing new targets for intervening with fibril formation. We have investigated fibril formation by hen egg white lysozyme, an enzyme for which human variants underlie non-neuropathic amyloidosis. Using a combination of static and dynamic light scattering, atomic force microscopy and circular dichroism, we find that amyloidogenic lysozyme monomers switch between three different assembly pathways: from monomeric to oligomeric fibril assembly and, eventually, disordered precipitation as the ionic strength of the solution increases. Fibril assembly only occurred under conditions of net repulsion among the amyloidogenic monomers while net attraction caused precipitation. The transition from monomeric to oligomeric fibril assembly, in turn, occurred as salt-mediated charge screening reduced repulsion among individual charged residues on the same monomer. We suggest a model of amyloid fibril formation in which repulsive charge interactions are a prerequisite for ordered fibril assembly. Furthermore, the spatial extent of non-specific charge screening selects between monomeric and oligomeric assembly pathways by affecting which subset of denatured states can form suitable intermolecular bonds and by altering the energetic and entropic requirements for the initial intermediates emerging along the monomeric vs. oligomeric assembly path.     

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.     

Investigation on the mechanism of crystallization of soluble protein in the presence of nonionic surfactant

The mechanism of crystallization of soluble, globular protein (lysozyme) in the presence of nonionic surfactant C8E4 (tetraoxyethylene glycol monooctyl ether) was examined using both static and dynamic light scattering. The interprotein interaction was found to be attractive in solution conditions that yielded crystals and repulsive in the noncrystallizing solution conditions. The validity of the second virial coefficient as a criterion for predicting protein crystallization could be established even in the presence of nonionic surfactants. Our experiments indicate that the origin of the change in interactions can be attributed to the adsorption of nonionic surfactant monomers on soluble proteins, which is generally assumed to be the case with only membrane proteins. This adsorption screens the hydrophobic attractive force and enhances the hydration and electrostatic repulsive forces between protein molecules. Thus at low surfactant concentration, the effective protein-protein interaction remains repulsive. Large surfactant concentrations promote protein crystallization, possibly due to the attractive depletion force caused by the intervening free surfactant micelles.     

Coarse-Grained Model of SNARE-Mediated Docking

Synaptic transmission requires that vesicles filled with neurotransmitter molecules be docked to the plasma membrane by the SNARE protein complex. The SNARE complex applies attractive forces to overcome the long-range repulsion between the vesicle and membrane. To understand how the balance between the attractive and repulsive forces defines the equilibrium docked state we have developed a model that combines the mechanics of vesicle/membrane deformation with an apparently new coarse-grained model of the SNARE complex. The coarse-grained model of the SNARE complex is calibrated by comparison with all-atom molecular dynamics simulations as well as by force measurements in laser tweezer experiments. The model for vesicle/membrane interactions includes the forces produced by membrane deformation and hydration or electrostatic repulsion. Combining these two parts, the coarse-grained model of the SNARE complex with membrane mechanics, we study how the equilibrium docked state varies with the number of SNARE complexes. We find that a single SNARE complex is able to bring a typical synaptic vesicle to within a distance of ∼3 nm from the membrane. Further addition of SNARE complexes shortens this distance, but an overdocked state of >4–6 SNAREs actually increases the equilibrium distance.     

Role of DNA-DNA interactions on the structure and thermodynamics of bacteriophages Lambda and P4

Electrostatic interactions play an important role in both packaging of DNA inside bacteriophages and its release into bacterial cells. While at physiological conditions DNA strands repel each other, the presence of polyvalent cations such as spermine and spermidine in solutions leads to the formation of DNA condensates. In this study, we discuss packaging of DNA into bacteriophages P4 and Lambda under repulsive and attractive conditions using a coarse-grained model of DNA and capsids. Packaging under repulsive conditions leads to the appearance of the coaxial spooling conformations; DNA occupies all available space inside the capsid. Under the attractive potential both packed systems reveal toroidal conformations, leaving the central part of the capsids empty. We also present a detailed thermodynamic analysis of packaging and show that the forces required to pack the genomes in the presence of polyamines are significantly lower than those observed under repulsive conditions. The analysis reveals that in both the repulsive and attractive regimes the entropic penalty of DNA confinement has a significant non-negligible contribution into the total energy of packaging. Additionally we report the results of simulations of DNA condensation inside partially packed Lambda. We found that at low densities DNA behaves as free unconfined polymer and condenses into the toroidal structures; at higher densities rearrangement of the genome into toroids becomes hindered, and condensation results in the formation of non-equilibrium structures. In all cases packaging in a specific conformation occurs as a result of interplay between bending stresses experienced by the confined polymer and interactions between the strands.     

THE INFLUENCE OF ELECTROLYTES ON THE ELECTRIFICATION AND THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES

1. When pure water is separated by a collodion membrane from a watery solution of an electrolyte the rate of diffusion of water is influenced not only by the forces of gas pressure but also by electrical forces. 2. Water is in this case attracted by the solute as if the molecules of water were charged electrically, the sign of the charge of the water particles as well as the strength of the attractive force finding expression in the following two rules, (a) Solutions of neutral salts possessing a univalent or bivalent cation influence the rate of diffusion of water through a collodion membrane, as if the water particles were charged positively and were attracted by the anion and repelled by the cation of the electrolyte; the attractive and repulsive action increasing with the number of charges of the ion and diminishing inversely with a quantity which we will designate arbitrarily as the "radius" of the ion. The same rule applies to solutions of alkalies. (b) Solutions of neutral or acid salts possessing a trivalent or tetravalent cation influence the rate of diffusion of water through a collodion membrane as if the particles of water were charged negatively and were attracted by the cation and repelled by the anion of the electrolyte. Solutions of acids obey the same rule, the high electrostatic effect of the hydrogen ion being probably due to its small "ionic radius." 3. The correctness of the assumption made in these rules concerning the sign of the charge of the water particles is proved by experiments on electrical osmose. 4. A method is given by which the strength of the attractive electric force of electrolytes on the molecules of water can be roughly estimated and the results of these measurements are in agreement with the two rules. 5. The electric attraction of water caused by the electrolyte increases with an increase in the concentration of the electrolyte, but at low concentrations more rapidly than at high concentrations. A tentative explanation for this phenomenon is offered. 6. The rate of diffusion of an electrolyte from a solution to pure solvent through a collodion membrane seems to obey largely the kinetic theory inasmuch as the number of molecules of solute diffusing through the unit of area of the membrane in unit time is (as long as the concentration is not too low) approximately proportional to the concentration of the electrolyte and is the same for the same concentrations of LiCl, NaCl, MgCl₂, and CaCl₂.     

Spatially resolved force spectroscopy of biological surfaces using the atomic force microscope

The spatial distribution of intermolecular forces governs macromolecular interactions. The atomic force microscope, a relatively new tool for investigating interaction forces between nanometer-scale objects, can be used to produce spatially resolved maps of the surface or material properties of a sample; these include charge density, adhesion and stiffness, as well as the force required to break specific ligand-receptor bonds. Maps such as these will provide fundamental insights into biological structure and will become an important tool for characterizing technologically important biological systems.