Dirk Stigter

MODELING PROTEIN STABILITY AS HETEROPOLYMER COLLAPSE

Publisher Summary This chapter reviews a simple model for the stabilities of globular proteins, called the heteropolymer collapse (HPC) model. It assumes that protein stability predominantly arises from the collapse of heteropolymeric chains of nonpolar and polar amino acids in water. The burial of nonpolar groups is opposed by configurational entropies and by electrostatic repulsions when proteins are in acids or bases. Although the model neglects helical propensities, ion pairing and other specific interactions, side-chain entropies and packing interactions, and—in its present version—burial of polar monomers, it predicts at least qualitatively several general properties of protein stability, including the dependences on temperature, denaturants, pH, and salts and radii of denatured states. For apomyoglobin, it predicts the phase boundaries for the three stable states-native, highly unfolded, and compact denatured states, as functions of temperature, pH, and salt. The model goes beyond isomer counting for chain entropies and beyond the assumption that denatured states are highly solvated random flights.

Evaluation of the counterion condensation theory of polyelectrolytes.

We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.

Binding of ionic ligands to polyelectrolytes

Ionic ligands can bind to polyelectrolytes such as DNA or charged polysaccharides. We develop a Poisson-Boltzmann treatment to compute binding constants as a function of ligand charge and salt concentration in the limit of low ligand concentration. For flexible chain ligands, such as oligopeptides, we treat their conformations using lattice statistics. The theory predicts the salt dependence and binding free energies, of Mg(2+) ions to polynucleotides, of hexamine cobalt(III) to calf thymus DNA, of polyamines to T7 DNA, of oligolysines to poly(U) and poly(a), and of tripeptides to heparin, a charged polysaccharide. One parameter is required to obtain absolute binding constants, the distance of closest separation of the ligand to the polyion. Some, but not all, of the binding entropies and enthalpies are also predicted accurately by the model.

Phospholipid interactions in model membrane systems. II. Theory

We describe statistical thermodynamic theory for the lateral interactions among phospholipid head groups in monolayers and bilayers. Extensive monolayer experiments show that at low surface densities, PC head groups have strong lateral repulsions which increase considerably with temperature, whereas PE interactions are much weaker and have no significant temperature dependence (see the preceding paper). In previous work, we showed that the second virial coefficients for these interactions can be explained by: (a) steric repulsions among the head groups, and (b) a tilting of the P-N+ dipole of PC so that the N+ end enters the oil phase, to an extent that increases with temperature. It was also predicted that PE interactions should be weaker and less temperature dependent because the N+ terminal of the PE head-group is hydrophilic, hence, it is tilted into the water phase, so dipolar contributions among PEs are negligible due to the high dielectric constant of water. In the present work, we broaden the theory to treat phospholipid interactions up to higher lateral surface densities. We generalize the Hill interfacial virial expansion to account for dipoles and to include the third virial term. We show that to account for the large third virial coefficients for both PC and PE requires that the short range lateral attractions among the head groups also be taken into account. In addition, the third virial coefficient includes fluctuating head group dipoles, computed by Monte Carlo integration assuming pairwise additivity of the instantaneous pair potentials. We find that because the dipole fluctuations are correlated, the average triplet interactions do not equal the sum of the average dipole pair potentials. This is important for predicting, the magnitude and the independence of temperature of the third virial coefficients for PC. The consistency of the theory with data of both the second and the third virial coefficients extends the applicability of the head-group model to semiconcentrated monolayers, in agreement with the surface potential data in the foregoing paper.

A Commentary on the Screened-Oseen, Counterion-Condensation Formalism of Polyion Electrophoresis

The use of linear theory, in particular, counterion condensation (CC) theory, in describing electrophoresis of polyelectrolyte chains, is criticized on several grounds. First, there are problems with CC theory in describing the equilibrium distribution of ions around polyelectrolytes. Second, CC theory is used to treat ion relaxation in a linear theory with respect to the polyion charge despite the fact that ion relaxation arises as a consequence of nonlinear charge effects. This nonlinearity has been well established by several investigators over the last 70 years for spherical, cylindrical, and arbitrarily shaped model polyions. Third, current use of CC theory ignores the electrophoretic hindrance as well as the ion relaxation for condensed counterions and only includes such interactions for uncondensed counterions. Because most of the condensed counterions lie outside the shear surface of the polyion (in the example of DNA), the assumption of ion condensation is artificial and unphysical. Fourth, the singular solution, based on a screened Oseen tensor, currently used in the above mentioned theories is simply wrong and fails to account for the incompressibility of the solvent. The actual singular solution, which has long been available, is discussed. In conclusion, it is pointed out that numerical alternatives based on classic electrophoresis theory (J.T.G. Overbeek, Kolloid-Beih, 1943, 54:287-364) are now available.

Theory for protein solubilities

Abstract Apomyoglobin is a protein that has a minimum in solubility as a function of urea concentration in water. We propose a mean-field model to account for this behavior. In contrast to the view that proteins aggregate in conformations intermediate between native and denatured states, the present model proposes that denatured states aggregate, and that the minimum in solubility arises from coupling of the aggregation equilibrium with the folding/unfolding equilibrium.

Wall effects on DNA stretch and relaxation

Hydrodynamic wall effects are treated with an image or reflection method. This method uses a mirror image of the molecule, with the opposite velocity, to satisfy the non-slip boundary condition of zero velocity of the liquid at the wall. Molecules moving inside a slit require an infinite series of images, or reflections from both walls, whose effects converge slower for thinner slits. It is shown that, with the same external field, wall effects increase the electrophoretic stretch of DNA, more so for thinner slits. The theory is in fairly good agreement with stretch experiments on T4 DNA in slits of width 5, 0.3, and 0.09 microm by Bakajin et al. (Phys. Rev. Let. 80 (1998) 2737). For the same slits relaxation data are available for T4 DNA first hooked around an obstacle, stretched in a U-shape in an external electric field, and sliding off until the stretched molecule moves away in free electrophoresis. The theory approximates the relaxation of the molecule, after detachment from the obstacle, as the relaxation of tethered DNA stretched in a temporary electric field. The theory agrees fairly well with the experiments. The significance of electroosmotic flow is discussed for electrophoretic experiments. An Appendix gives numerical data on the free electrophoresis of unstained and stained DNA, and discusses problems of the kinetic diameter of DNA.

Donnan membrane equilibrium, sedimentation equilibrium, and coil expansion of DNA in salt solutions.

This is a review of applications of the McMillan-Mayer-Hill virial theory and the ionic double-layer theory to dilute colloidal solutions, in particular, solutions of DNA. Interactions of highly charged colloidal rods are developed in terms of the second virial coefficients between two rods, and between one rod and one small co-ion. The relevant cluster integrals are evaluated with interaction potentials based on the Poisson-Boltzmann equation. The treatment is extended to the intrachain repulsion responsible for the statistical swelling of coiled DNA (excluded volume effect). The theory is compared with three sets of experimental data: The salt distribution in Donnan membrane equilibria of DNA-salt solutions, sedimentation equilibria of short DNA fragments at different ionic strengths, and the intrinsic viscosity of T7 DNA in NaCl solutions. In all cases the theory agrees well with the experiments. The agreement is not convincing for the sedimentation equilibrium at low ionic strength, because here the experimental DNA concentration is too high for the truncated dilute solution expansion of the DNA-salt repulsion.

An electrostatic model of B-DNA for its stability against unwinding

In single molecule experiments Smith et al. (Science 271 (1996) 795) have unwound the B-DNA helix by stretching it in an aqueous salt solution. They found that the stretching force required for the transition decreases significantly with lowering of the salt concentration. We show that the observed salt effect is consistent with a uniformly charged cylinder model of DNA surrounded by a Poisson-Boltzmann ionic atmosphere. We also derive a simple connection between the sharpness of the center part of the transition and its cooperativity in terms of an average block size of base pairs that unwinds or rewinds.