Effects of molecular crowding on stretching of polymers in poor solvent

Structure and Dynamics of dsDNA in Cell-like Environments

Deoxyribonucleic acid (DNA) is a fundamental biomolecule for correct cellular functioning and regulation of biological processes. DNA's structure is dynamic and has the ability to adopt a variety of structural conformations in addition to its most widely known double-stranded DNA (dsDNA) helix structure. Stability and structural dynamics of dsDNA play an important role in molecular biology. In vivo, DNA molecules are folded in a tightly confined space, such as a cell chamber or a channel, and are highly dense in solution; their conformational properties are restricted, which affects their thermodynamics and mechanical properties. There are also many technical medical purposes for which DNA is placed in a confined space, such as gene therapy, DNA encapsulation, DNA mapping, etc. Physiological conditions and the nature of confined spaces have a significant influence on the opening or denaturation of DNA base pairs. In this review, we summarize the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions. We include studies on various thermal and mechanical properties of dsDNA in ionic solutions, molecular crowded environments, and confined spaces. By providing a better understanding of melting and unzipping of dsDNA in different environments, this review provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.

Diameter Dependent Melting and Softening of dsDNA Under Cylindrical Confinement

Carbon nanotubes (CNTs) are considered promising candidates for biomolecular confinement, including DNA encapsulation for gene delivery. Threshold values of diameters have been reported for double-stranded DNA (dsDNA) encapsulation inside CNTs. We have performed all-atom molecular dynamics (MD) simulations of dsDNAs confined inside single-walled CNTs (SWCNTs) at the physiologically relevant temperature of 300 K. We found that the dsDNA can be confined without being denatured only when the diameter of the SWCNT exceeds a threshold value. Below this threshold diameter, the dsDNA gets denatured and melts even at the temperature of 300 K. Our simulations using SWCNTs with chirality indices (20,20) to (30,30) at 300 K found the critical diameter to be 3.25 nm (corresponding to (24,24) chirality). Analyses of the hydrogen bonds (H-bonds), Van der Walls (VdW) energy, and other inter-base interactions show drastic reduction in the number of H-bonds, VdW energy, and electrostatic energies between the bases of dsDNA when it is confined in narrower SWCNTs (up to diameter of 3.12 nm). On the other hand, the higher interaction energy between the dsDNA and the SWCNT surface in narrower SWCNTs assists in the melting of the dsDNA. Electrostatic mapping and hydration status analyses show that the dsDNA is not adequately hydrated and the counter ion distribution is not uniform below the critical diameter of the SWCNT. As properly hydrated counter ions provide stability to the dsDNA, we infer that the inappropriate hydration of counter ions and their non-uniform distribution around the dsDNA cause the melting of the dsDNA inside SWCNTs of diameter below the critical value of 3.25 nm. For confined dsDNAs that do not get denatured, we computed their elastic properties. The persistence length of dsDNA was found to increase by a factor of about two and the torsional stiffness by a factor of 1.5 for confinement inside SWCNTs of diameters up to 3.79 nm, the stretch modulus also following nearly the same trend. Interestingly, for higher diameters of SWCNT, 3.79 nm and above, the dsDNA becomes more flexible, demonstrating that the mechanical properties of the dsDNA under cylindrical confinement depend non-monotonically on the confinement diameter.

Dynamics of a polymer chain translocating through varying cone-shaped channels

By employing the exact enumeration technique, we study consequences of different apex angles of a wedge-shaped channel on the mean first passage time and free-energy profile of a linear polymer chain translocating from the cis- to the trans-side through an interacting pore. We investigate effects of asymmetry arising in the free-energy profile due to the change in apex angles and its dependence on the first passage time. We report the combined effect of entropy (arising due to apex angles) and pore interaction on the nonmonotonic behavior of the translocation time. The effect of different solvent quality across the channel has also been explored. We show that the increase in monomer-monomer interaction leads to the formation of globules near the pore, which drives the process faster.

Polymer in wedge-shaped confinement: Effect on the θ temperature

The equilibrium properties of a finite-length linear polymer chain confined in an infinite wedge composed of two perfectly reflecting hard walls meeting at a variable apex angle (α) are presented. One end of the polymer is anchored a distance y from the apex on the conical axis of symmetry, while the other end is free. We report here, the nonmonotonic behavior of θ temperature as a function of y for a finite-length chain. Data collapse for different chain lengths indicates that such behavior will exist for all finite lengths. We delineate the origin of such nonmonotonic behavior, which may have potential applications in understanding the cellular process occurring in nanoconfined geometries.

DNA melting in the presence of molecular crowders

We study the opening of double stranded DNA (dsDNA) in the presence of molecular crowders using the Peyrard–Bishop–Dauxois (PBD) model.

Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters

We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks of over 10^{4} steps, far more than has ever been possible. The scaling exponent ν for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. We find strong evidence against the widely assumed scaling law for the number of conformations and propose an alternative, which perfectly fits our data.

Ring polymers in crowded environment: conformational properties

We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law ~r(-a) is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius ⟨R(g ring)⟩ and spanning radius ⟨R(1/2 ring)⟩ of typical ring polymer conformation up to the first order of double ɛ = 4 - d, δ = 4 - a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to ⟨R(g ring)(2)⟩/⟨R(g chain)(2)⟩=½(1+(13/48)δ).

Equivalence of quenched and annealed averaging in models of disordered polymers

The equivalence of the influence of quenched and annealed disorder on the scaling properties of long flexible polymer chains is proved by analyzing the O(m)-symmetric field theory in the polymer (de Gennes) limit m → 0. Additional symmetry properties of the model in this limit are discussed.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.

Constrained random-force model for weakly bending semiflexible polymers

The random-force (Larkin) model of a directed elastic string subject to quenched random forces in the transverse directions has been a paradigm in the statistical physics of disordered systems. In this Brief Report, we investigate a modified version of the above model where the total transverse force along the polymer contour and the related total torque, in each realization of disorder, vanish. We discuss the merits of adding these constraints and show that they leave the qualitative behavior in the strong stretching regime unchanged, but they reduce the effects of the random force by significant numerical prefactors. We also show that a transverse random force effectively makes the filament softer to compression by inducing undulations. We calculate the related linear compression coefficient in both the usual and the constrained random-force model.

Polymers in crowded environment under stretching force: Globule-coil transitions

We study flexible polymer macromolecules in a crowded (porous) environment, modeling them as self-attracting self-avoiding walks on site-diluted percolative lattices in space dimensions d=2,3 . The influence of stretching force on the polymer folding and the properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method, we estimate the transition temperature TTheta between collapsed and extended polymer configurations and construct the phase diagrams of the globule-coil coexistence when varying temperature and stretching force. The transition to a completely stretched state, caused by applying force, is discussed as well.

Force induced unfolding of biopolymers in a cellular environment: a model study

Effect of molecular crowding and confinement experienced by protein in the cell during unfolding has been studied by modeling a linear polymer chain on a percolation cluster. It is known that internal structure of the cell changes in time, however, they do not change significantly from their initial structure. In order to model this we introduce the correlation among the different disorder realizations. It was shown that the force-extension behavior for correlated disorder in both constant force ensemble and constant distance ensemble is significantly different than the one obtained in absence of molecular crowding.