Comment on the Letter by A. Ben-Shaul: “Entropy,Energy, and Bending of DNA in Viral Capsids”

The conformational entropic penalty associated with packaging double-stranded DNA into viral capsids remains an issue of contention. So far, models based on a continuum approximation for DNA have either left the question unexamined, or they have assumed that the entropic penalty is negligible, following an early analysis by Riemer and Bloomfield. In contrast, molecular-dynamics (MD) simulations using bead-and-spring models consistently show a large penalty. A recent letter from Ben-Shaul attempts to reconcile the differences. While the letter makes some valid points, the issue of how to include conformational entropy in the continuum models remains unresolved. In this Comment, I show that the free energy decomposition from continuum models could be brought into line with the decomposition from the MD simulations with two adjustments. First, the entropy from Flory-Huggins theory should be replaced by the estimate of the entropic penalty given in Ben-Shaul’s letter, which corresponds closely to that from the MD simulations. Second, the DNA-DNA repulsions are well described by the empirical relationship given by the Cal Tech group, but the strength of these should be reduced by about half, using parameters based on the Rau-Parsegian experiments, rather than treating them as “fitting parameters (tuned) to fit the data from (single molecule pulling) experiments.”     

Entropy,Energy, and Bending of DNA in Viral Capsids

Inspired by novel single-molecule and bulk solution measurements, the physics underlying the forces and pressures involved in DNA packaging into bacteriophage capsids became the focus of numerous recent theoretical models. These fall into two general categories: Continuum-elastic theories (CT), and simulation studies—mostly of the molecular dynamics (MD) genre. Both types of models account for the dependence of the force, and hence the packaging free energy (ΔF), on the loaded DNA length, but differ markedly in interpreting their origin. While DNA confinement entropy is a dominant contribution to ΔF in the MD simulations, in the CT theories this role is fulfilled by interstrand repulsion, and there is no explicit entropy term. The goal of this letter is to resolve this apparent contradiction, elucidate the origin of the entropic term in the MD simulations, and point out its tacit presence in the CT treatments.The genomic double-stranded (ds) DNA inside bacteriophage heads is highly stressed, leading to internal pressures of up to ∼50 atmospheres, reflecting the tight packing and extreme bending of this highly charged and rigid molecule (1). The interaxial distance (d) between neighboring (nonbonded) dsDNA segments in the fully packaged virus is typically ≈2.5 nm (2,3), just slightly larger than the hardcore diameter of dsDNA (b = 2.0 nm) and well into the repulsive regime (d ≤ 2.8 nm) of DNA-DNA interaction in ionic solutions (4–6). Moreover, free dsDNA in (physiological) solution is a fluctuating, semiflexible, wormlike chain (WLC), with persistence length ξ ≈ 50 nm, larger than the radius of most viral capsids. Thus, on a molecular scale, packaging the long (e.g., the 330-ξ long λ-phage genome) viral DNA into its tiny capsid requires enormous mechanical work.The force needed to package the DNA is provided by an ATP-driven motor protein situated at the capsid portal. Recent single molecule measurements reveal that this force, f(L_int), increases sharply with the loaded genome length, L_int, rising to ∼30–100 pN, depending on the virus in question (7,8). These studies inspired the formulation of many theoretical models of DNA packaging in viral capsids, which fall roughly into two categories:     

Reply to “Commentary on Photosynthesis and Negative Entropy Production by Jennings and coworkers” by J. Lavergne

It is argued that the chemical potential analogy does not provide useful information on the thermodynamics of photosystems, as the thermodynamic efficiency of an absorbed quantum is not considered. Instead, the approach based on either entropy balance or entropy flux considerations does provide this information. At high thermodynamic efficiencies, primary photochemistry can, in principle, violate the Second Law of Thermodynamics.     

On “Entropy consumption in primary photosynthesis” by Jennings et al.

The preceding paper [R.C. Jennings, E. Belgio, A.P. Casazza, F.M. Garlaschi, G. Zucchelli, Entropy consumption in primary photosynthesis, Biochim. Biophys. Acta (in press)] is criticized on several grounds.     

Bending of the “9+2” axoneme analyzed by the finite element method

Many data demonstrate that the regulation of the bending polarity of the “9+2” axoneme is supported by the curvature itself, making the internal constraints central in this process, adjusting either the physical characteristics of the machinery or the activity of the enzymes involved in different pathways. Among them, the very integrated Geometric Clutch model founds this regulation on the convenient adjustments of the probability of interaction between the dynein arms and the β-tubulin monomers of the outer doublet pairs on which they walk. Taking into consideration (i) the deviated bending of the outer doublets pairs (Cibert, C., Heck, J.-V., 2004. Cell Motil. Cytoskeleton 59, 153-168), (ii) the internal tensions of the radial spokes and the tangential links (nexin links, dynein arms), (iii) a theoretical 5 μm long proximal segment of the axoneme and (iv) the short proximal segment of the axoneme, we have reevaluated the adjustments of these intervals using a finite element approach. The movements we have calculated within the axonemal cylinder are consistent with the basic hypothesis that found the Geometric Clutch model, except that the axonemal side where the dynein arms are active increases the intervals between the two neighbor outer doublet pairs. This result allows us to propose a mechanism of bending reversion of the axoneme, involving the concerted ignition of the molecular engines along the two opposite sides of the axoneme delineated by the bending plane.