Phase diagram of the ground states of DNA condensates

Abstract

Phase diagram of the ground states of DNA in a bad solvent is studied for a semi-flexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter x and effective self-attraction promoting compaction. x = 1 corresponds to the worm-like chain model. Surprisingly, the phase diagram as well as the transition lines between the ground states are found to be a function of x. The model provides a simple explanation for the results of prior experimental and computational studies and makes predictions for the specific geometries of the ground states. The results underscore the impact of the form of the microscopic bending energy at macroscopic observable scales.The non-linear elasticity of DNA at short length scales, probed by non-equilibrium DNA cyclization experiments [1,2], AFM imaging on surfaces [3], as well as by equilibrium mechanically constrained DNA experiments [4][5][6], is still not well understood. While the conclusions regarding the first two methods for probing non-linear ds-DNA elasticity have been criticized [7], the experiments on stressed DNA ring molecules are performed by a different methodology based on thermodynamic methods via DNA high-curvature states through partial hybridization of a ss-DNA loop with a linear complementary strand [6]. This methodology does not depend on thermal fluctuations to realize high-curvature states and thus appears to have a far better accuracy and reliability. The non-linearity in this latter case is clearly present and is captured in a single parameter describing the onset of DNA kink formation. This clearly exhibited elastic nonlinearity is taken as the motivation for the present study that attempts to derive the macroscopic consequences of this interesting microscopic elastic behavior of DNA.Another interesting facet of DNA behavior is that under specific solution conditions, it condenses into highly compact structures with pronounced symmetry [8][9][10][11]. This condensation phenomenon serves as an example of high polymer density packing in biology and of polymer phase transitions and phase separations in general, being relevant also for artificial gene delivery [12,13]. Several distinct morphologies of the DNA condensates have been observed including a toroid, a spheroid as well as a rodlike configuration [10,[14][15][16]. Our principal goal is to explore the rich interplay between the strong tendency for compactness, arising from the presence of multivalent cations or osmolytes in the solution, and the intrinsic stiffness of the DNA molecule promoting the chain to be locally straight. In the absence of stiffness, one would expect the chain to adopt a densely compact spheroidal globule configuration. The key issue is to understand how local stiffness and the detailed way it enters the elastic energy result in the spheroidal configuration becoming unstable w.r.t. other lower energy configurations. In particular, one would like to map out a phase diagram and understand the different condensate geometries.The topolog...

Effective stiffness and formation of secondary structures in a protein-like model

“…In the U θ0 model, a toroidal phase is observed, clearly distinct from a helical phase. This agrees with previous findings within the DNA condensation framework [11,12]. By contrast, no such toroidal phase is observed in the OP model with the same stiffness.…”

“…For higher bending rigidity and in the absence of side chains, the U θ0 model displays toroidal phases as it was found in Refs. [11,12] This means that explicit energetic bending rigidity is not compatible with secondary structures typically found in proteins, even in the presence of side chains. This notwithstanding, it is still noteworthy that the U θ0 model with side chains and the OPSC share the same phenomenology at intermediate temperatures in terms of an effective stiff coil conformation, and that this is true whether or not side chains are present.…”

“…A typical example of stiff biopolymer is provided by DNA, whose hybridized double strand form has a persistence length typically 100 times larger than that corresponding to each single strand [7]. This property affects the corresponding phase diagram whose collapsed phase is found to be either a toroid or a rod-like phase, unlike the zero-stiffness flexible case, that is found to be a compact globule [8][9][10][11][12].…”

Generalized conservation law for main-chain polymer nematics

“…In this note we address and resolve all these fundamental questions for future applications. In fact, we show that the two conservation laws are not equivalent, are irreducible and in general lead to different consequences specifically stemming from the presence of the backfolding configurations of the polymer chains, or in an extreme case, to the presence of localized hairpins and/or kinks which should be in particular relevant in the description of confined DNA mesophases, where such local defects or elastic energy non-linearities have been implicated recently [12].…”

Chain stiffness bridges conventional polymer and bio-molecular phases

“…This includes, for instance double stranded DNA [11] for which the persistence length is known to be 150bp (equivalent to ≈ 50nm). The WLC model fully accounts for the experimental findings in DNA condensation that can be easily rationalized in terms of competition between the hydrophobic effect, promoting compaction, and the bending rigidity, tending to oppose it [12,13]. We will refer to this more conventional stiffness as energetic, in order to distinguish it from the entropic one.…”