The Section on Molecular Biophysics examines the organization of molecular assemblies. Its current purview includes DNA/lipid assemblies; DNA assemblies such as are seen in viral capsids and in vitro; polypeptides and polysaccharides; and lipid/water systems. In all these systems, we measure intermolecular forces or interaction energies. We would like to characterize and codify measured forces in order to build a practical molecular physics of living systems. Our undertaking is strengthened by its strong connection with physical theory, in particular statistical mechanics applied to liquid crystals and to complex fluids.

Because intermolecular forces act in liquids and depend on temperature, salts, solutes, and specific ligands, we speak of them as thermodynamic. These forces are the spatial derivatives of the free energies whose temperature derivatives are entropies. Changes in the entropies with water chemical potential reveal hydration; an "excess" or "deficit" of the dependence of the changes on solute chemical potentials indicate solute attraction or repulsion. Thus, we can think of the changes as direct (i.e., electrostatic, van der Waals, or hydration forces) or as indirect (i.e., acting through changes in the free energy of both translation and configuration of concentrated macromolecules).

Molecular Gymnastics
Hansen, Podgornik, Parsegian
Understandably popular with molecular biologists, DNA has attained almost "most popular macromolecule" status among physicists. Except for simple synthetic polymers and proteins, DNA garners the most attention. Limited enough in its contortions yet tough enough to endure manipulative tortures, DNA inspires physicists. For years, we have been measuring forces between DNA double helices and formulating theories to describe these interactions. Now, with access to measurements of the elastic properties of single DNA molecules, we have begun to connect what we have learned about forces between molecules to forces within them.

When not packed into chromatin and allowed to spread out, DNA reveals its electrical charge and its inherent flexibility. Crowded by competition with other polymers or drenched in neutralizing salts, DNA resists compaction by hanging onto its waters of solvation, what we see as hydration forces. Exposed to multivalent "condensing" ions such as spermine, both in vivo and in vitro, a large DNA molecule collapses on itself or assembles with other DNA molecules. The assembly and interaction of this informational molecule teach us lessons about, for example, DNA/protein binding (see Don Rau et al. Intermolecular forces, recognition, and dynamics), DNA packing into viruses, DNA/lipid interactions in transfection systems, and virtually every event where DNA must be unpackaged to be read. The past year or so has yielded the following information.

The osmotic pressure of B-DNA in dilute solutions deviates by as much as 100 percent from predictions based on a widely accepted counterion condensation theory. We found that a cell model description of the ionic atmosphere near a cylindrical polyelectrolyte predicts osmotic properties that are in surprisingly good harmony with all available experimental findings over a wide range of DNA concentrations. We were able to argue that the neglect of molecular features, such as finite radius, makes the popular condensation theory inapplicable at all but impractically low polyelectrolyte concentrations.

When pulled almost straight by using molecular tweezers, DNA and other electrically charged molecules are more easily stretched than expected from their usual spring constant. The phenomenon is termed elastic moduli renormalization in self-interacting stretchable polyelectrolytes and may be explained by the following analogy. When you pull on a wiggly spring, most of the work goes into straightening. When near straightness, the spring material itself must become longer. If the material contains many electrical charges, e.g., the phosphates on the backbone of DNA, and there is not enough salt in the bathing solution to screen the interactions of the charges, then repulsion between charges on the molecule makes the spring easier to stretch. This is not obvious. It must be that the repulsion between charges drops off at a different rate than the elastic forces within the bonds that hold the molecule together. We were able to demonstrate when DNA experiments would meet these conditions. In fact, recent single-molecule-stretching data from the laboratory of Victor Bloomfield in Minnesota confirms our theoretical predictions. We have changed the way people connect the elastic properties of flexible polyelectrolytes with solution conditions. The lessons can be extended to two-dimensional membranes as well (Podgornik et al.,2000).

And speaking of dimensions, we can express the dimension of a linear molecule in terms of the way it fills space. We have examined the contortions of wormlike chains, i.e., linear molecules that require energy to be twisted, bent, or stretched, from the perspective of how they fill space. We already know that the size of a totally stiff chain grows in proportion to the chain's length but that a totally flexible chain curls up into a scrambled mess whose average radius grows in proportion to the square root of the chain's length. However, the addition of finite stiffness and, better, interactions between segments of the chain reveals that the chain/molecule fills space according to the range and strength of segmental interactions. Measurements such as dynamic light scattering allow us to compare changes in measured molecular sizes with the changes in intersegmental interactions caused by solution conditions.

The Entropically Favored Compression of Sickle Cell Hemoglobin Gels, Protein-Water Interactions
Chik, Parsegian
Contrary to the popular and accurate "hard-sphere" depiction of normal hemoglobin in solution or in a red cell, sickle cell hemoglobin requires attention to molecular interactions. The reason is that deoxygenated hemoglobin aggregates into long rods or "gels" that grow to deform and stiffen red cells so that the cells cannot wriggle through capillaries. One of the remarkable features of the gels is that they form more easily at higher temperature. Several years ago, we put some HbS solutions in a dialysis bag and shrank it by dipping the bag in high-concentration solutions of dextran. The HbS solutions concentrated under the osmotic stress of the dextran solution. Then, at a well-defined osmotic pressure, the HbS suddenly collapsed into the gel. Collapse required less pressure at higher temperature. From the increasing ease of collapse, we were able to extract an "entropy" of gelation, which is the change in the number of ways the molecules can move when the proteins suddenly collapse. Moreover, "entropy" increased while the proteins were concentrated. Because the act of concentrating proteins is also an act of squeezing out water from the protein solution, the immediate implication is that the squeezed-out waters enjoy more freedom to move.

Subject to greater-than-collapse pressures, the gel continued to shrink. This year, we realized that we could also measure the continuous change in entropy during the further concentration of the gels. For each water molecule removed, there is a four-fold increase in the entropy of compression compared with that occurring during initial formation of the gel. It seems that the act of gel compression differs from gel formation. What are the implications? Most models of the sickling event assume that the initial formation of the gel is the dominant, interesting event. From what we can tell, the compression of the gel merits attention. Small aggregates of molecules merge into large aggregates; the result is a progressively stable and stubborn knot of proteins. What we see with aggregating HbS resembles other temperature-driven aggregations, e.g., collagen and Mn DNA, that we have previously studied. Similarities in nominally different systems may point to a novel and ignored mechanism by which nature harnesses the normally disordering power of entropy to form complex higher-order structures from the interaction of intricately structured macromolecular surfaces.

Ion Counting
Hansen, Rau, Parsegian
Among the more important issues in molecular assembly is whether the forces between large charged molecules such as DNA result from hydration rather than from electrostatic forces. Hydration and electrostatic forces respond differently to solution conditions, particularly salts in the bathing medium. DNA-DNA forces are exceedingly sensitive to the concentration and type of positive ions to which they are exposed. The problem is that hydration and charge of interaction are of similar magnitude at high DNA densities. The two conditions vary differently as a function of separation but not enough to be discerned. However, electrostatic double layers depend on salt concentration in a different manner than do hydration forces, which, after all, act between neutral as well as between charged surfaces and have a screening length that does not depend on salt concentration.

We have begun using an "ion-counting" strategy developed in our laboratory. The strategy permits the change in measured forces with salt concentration to reveal the numbers and types of ions attracted to and repelled from the DNA. The numbers can be compared with the predictions of various theories as well as with the predictions of computer simulations to provide more critical tests than previously possible.

Measurements over the past year suggest that, at high salt concentration, DNA-DNA interactions are not electrostatic while, in the limit of low salt concentration, when the molecules are nearly in contact, the interaction is approximately 25 to 40 percent electrostatic, with the remainder attributable to hydration. Different anions and cations change the ratio.