We calculate the forces required to package (or, equivalently, acting to eject) DNA into (from) a bacteriophage capsid, as a function of the loaded (ejected) length, under conditions for which the DNA is either self-repelling or self-attracting. Through computer simulation and analytical theory, we find the loading force to increase more than 10-fold (to tens of piconewtons) during the final third of the loading process; correspondingly, the internal pressure drops 10-fold to a few atmospheres (matching the osmotic pressure in the cell) upon ejection of just a small fraction of the phage genome. We also determine an evolution of the arrangement of packaged DNA from toroidal to spool-like structures.T he classic Hershey-Chase experiment (1) of almost 50 years ago is best known for confirming DNA as the genetic material. But it was significant also as the demonstration that a bacterial virus (phage) leaves its protein capsid outside the cell it infects. More explicitly, upon binding to its receptor protein in the outer membrane of the bacterial cell, the viral capsid is opened and its DNA is injected into the cytoplasm. Obviously, this transfer can only happen as a passive process if the DNA is sufficiently pressurized in the capsid. For the past several decades, a great deal of experimental work has been devoted to determining the arrangement of ''packaged'' DNA in phage capsids through techniques that include x-ray scattering (2, 3), Raman spectroscopy (4), chemical cross-linking (5, 6), and electron microscopy (7,8,9). Various competing models have been proposed in which the DNA molecule is organized in concentric rings as a ''spool'' (3), in parallel segments joined at sharp kinks (10), or as a folded toroid (11). The most recent electron microscopy results on bacteriophages T7 (8) and T4 (9) show concentric ring structures that lend support to a spool-like structural motif. The underlying theoretical problem is also formidable, because one is confronted with the statistical-mechanical challenge of accounting for how a semif lexible, highly charged chain can be confined in dimensions comparable to its persistence length and yet hundreds of times smaller than its overall (contour) length L (12, 13). Although some estimates have been made of the pressure and elastic stress in a fully loaded capsid (12, 14), we are not aware of any attempt to treat the driving pressures during the course of ejection or the loading forces as a function of the extent of packaging (15). ¶In the present work, we connect the processes of loading DNA into, and ejecting it from, a phage capsid by calculating the energy of the chain as a function of the degree of loading or ejection. As already mentioned, the initial ejection is a passive process, being driven directly by the pressure difference inside and outside the capsid (16).ʈ Indeed, we shall show that the energy decreases monotonically as successively shorter lengths of DNA are left confined in the capsid; this rate of decrease corresponds to a force driving the chain outside. By ...

In a previous communication (Kindt et al., 2001) we reported preliminary results of Brownian dynamics simulation and analytical theory which address the packaging and ejection forces involving DNA in bacteriophage capsids. In the present work we provide a systematic formulation of the underlying theory, featuring the energetic and structural aspects of the strongly confined DNA. The free energy of the DNA chain is expressed as a sum of contributions from its encapsidated and released portions, each expressed as a sum of bending and interstrand energies but subjected to different boundary conditions. The equilibrium structure and energy of the capsid-confined and free chain portions are determined, for each ejected length, by variational minimization of the free energy with respect to their shape profiles and interaxial spacings. Numerical results are derived for a model system mimicking the lambda-phage. We find that the fully encapsidated genome is highly compressed and strongly bent, forming a spool-like condensate, storing enormous elastic energy. The elastic stress is rapidly released during the first stage of DNA injection, indicating the large force (tens of pico Newtons) needed to complete the (inverse) loading process. The second injection stage sets in when approximately 1/3 of the genome has been released, and the interaxial distance has nearly reached its equilibrium value (corresponding to that of a relaxed torus in solution); concomitantly the encapsidated genome begins a gradual morphological transformation from a spool to a torus. We also calculate the loading force, the average pressure on the capsid's walls, and the anisotropic pressure profile within the capsid. The results are interpreted in terms of the (competing) bending and interaction components of the packing energy, and are shown to be in good agreement with available experimental data.

The iron K-edge X-ray absorption spectrum of Rhodococcus sp. R312 (formerly Brevibacterium sp. R312) nitrile hydratase in frozen solutions at pH 7 and 9 has been analyzed to determine details of the iron coordination. EXAFS analysis implies two or three sulfur ligands per iron and overall six coordination; together with previous EPR and ENDOR results, this implies an N3S2O ligation sphere. The bond lengths from EXAFS analysis [rav(Fe-S) = 2.21 A at pH 7.3; rav(Fe-N/O) = 1.99 A] support cis coordination of two cysteine ligands and conclusively rule out nitric oxide coordination to the iron, a possibility proposed on the basis of an FTIR difference experiment [Noguchi, T., Honda, J., Nagamune, T., Sasabe, H., Inoue, Y., & Endo, I. (1995) FEBS Lett. 358, 9-12]. The higher-frequency EXAFS can be simulated well by inclusion of multiple scattering from two or three imidazole ligands; the fit to the data is improved if first-sphere multiple scattering pathways are also included. A slight shortening (by 0.02 +/- 0.01 A) of one or both Fe-S bonds when the pH is raised from 7.3 to 9.0 is consistent with shifts observed in the Raman spectrum [Brennan et al. (1996) Biochemistry 35, 10068-10077].