Aggregation dynamics of rigid polyelectrolytes

Sliding Dynamics of a Small Charged Ring Chain on the Diblock Polyelectrolyte in Poly[2]catenane in the Presence of Counterions

In this study, we investigate the sliding dynamics of small charged ring chains along the rigid central cyclic diblock polyelectrolyte of AnBn in radial charged poly[2]catenane in the presence of counterions using molecular dynamics simulations and the Lifson-Jackson formula, and our aim is to study the effects of electrostatical interaction strength, the size of the charged small ring chain, and the rigid block length of the diblock polyelectrolyte on the sliding dynamics of a small ring chain threaded on the rigid diblock polyelectrolyte. The mean-square displacement g3(t) of a small ring chain sliding along the rigid diblock polyelectrolyte of A10B10 exhibits oscillating behavior at short time scales for the moderate electrostatical interaction strength, while for the weak or strong electrostatic interactions, it is normal subdiffusion at short time scales. For n = 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock polyelectrolyte of A1B1 decreases monotonically as the relative electrostatic interaction strength A increases from A = 0.25-4. However, for n ≠ 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock polyelectrolyte of AnBn first decreases and then increases with the increase of A, and the nonmonotonous relationship between D and A becomes more obvious for larger n. In view of the free energy potential, the sliding diffusion of a small ring chain is governed by both the width of the free energy potential well and the height of the free energy potential barrier. According to the potential of mean force (PMF) of the small ring chain sliding along the rigid diblock polyelectrolyte, we find that our results are in good agreement with the theoretical analysis using the Lifson-Jackson formula. These results may help us to understand the diffusion motion of a ring chain in radial poly[n]catenanes from a fundamental point of view and control the sliding dynamics in molecular designs.

The conformational phase diagram of charged polymers in the presence of attractive bridging crowders

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase.

Lattice models for ballistic aggregation: Cluster-shape-dependent exponents

We study ballistic aggregation on a two-dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: In the first the aggregates remain point particles, in the second they retain the fractal shape at the time of collision, and in the third they assume a spherical shape. The exponents describing the power-law temporal decay of number of particles and energy as well as dependence of velocity correlations on mass are determined using large-scale Monte Carlo simulations. It is shown that the exponents are universal only for the point-particle model. In the other two cases, the exponents are dependent on the initial number density and correlations vanish at high number densities. The fractal dimension for the second model is close to 1.49.

DNA-protamine condensates under low salt conditions: molecular dynamics simulation with a simple coarse-grained model focusing on electrostatic interactions

Protamine, a small, strongly positively-charged protein, plays a key role in achieving chromatin condensation inside sperm cells and is also involved in the formulation of nanoparticles for gene therapy and packaging of mRNA-based vaccines against viral infection and cancer. The detailed mechanisms of such condensations are still poorly understood especially under low salt conditions where electrostatic interaction predominates. Our previous study, with a refined coarse-grained model in full consideration of the long-range electrostatic interactions, has demonstrated the crucial role of electrostatic interaction in protamine-controlled reversible DNA condensation. Therefore, we herein pay our attention only to the electrostatic interaction and devise a coarser-grained bead-spring model representing the right linear charge density on protamine and DNA chains but treating other short-range interactions as simply as possible, which would be suitable for real-scale simulations. Effective pair potential calculations and large-scale molecular dynamics simulations using this extremely simple model reproduce the phase behaviour of DNA in a wide range of protamine concentrations under low salt conditions, again revealing the importance of the electrostatic interaction in this process and providing a detailed nanoscale picture of bundle formation mediated by a charge disproportionation mechanism. Our simulations also show that protamine length alters DNA overcharging and in turn redissolution thresholds of DNA condensates, revealing the important role played by entropies and correlated fluctuations of condensing agents and thus offering an additional opportunity to design tailored nanoparticles for gene therapy. The control mechanism of DNA-protamine condensates will also provide a better microscopic picture of biomolecular condensates, i.e., membraneless organelles arising from liquid-liquid phase separation, that are emerging as key principles of intracellular organization. Such condensates controlled by post-translational modification of protamine, in particular phosphorylation, or by variations in protamine length from species to species may also be responsible for the chromatin-nucleoplasm patterning observed during spermatogenesis in several vertebrate and invertebrate species.

The effect of explicit polarity on the conformational behavior of a single polyelectrolyte chain

In this work using dissipative particle dynamics simulations with explicit treatment of polar species we demonstrate that the molecular nature of dielectric media has a significant impact on swelling and collapse of a polyelectrolyte chain in a dilute solution. We show that the small-scale effects related to the presence of polar species lead to the intensification of the electrostatic interactions when the charges are close to each other and/or their density is high enough. As a result, the electrostatic strength , usually regarded as the main parameter governing the polyelectrolyte chain collapse, does not have a universal meaning: the value of λ at which the coil-to-globule transition occurs is found to be dependent on the specific fixed value of the solvent bulk permittivity ε while varying the monomer unit charge Q and vice versa. This effect is observed even when the backbone and the counterions have the same polarity as the solvent beads, i.e. no dielectric mismatch is present. The reason for such behavior is rationalized in terms of the "effective" dielectric permittivity ε^eff which depends on the volume fraction φ of charged units inside the polymer chain volume; using ε^eff instead of ε collapses all data onto one master curve describing the chain shrinking with λ. Furthermore, it is shown that a polar chain adopts less swollen conformations in the polyelectrolyte regime and collapses more easily compared to a non-polar chain.

Protamine-Controlled Reversible DNA Packaging: A Molecular Glue

Packaging paternal genome into tiny sperm nuclei during spermatogenesis requires 10⁶-fold compaction of DNA, corresponding to a 10-20 times higher compaction than in somatic cells. While such a high level of compaction involves protamine, a small arginine-rich basic protein, the precise mechanism at play is still unclear. Effective pair potential calculations and large-scale molecular dynamics simulations using a simple idealized model incorporating solely electrostatic and steric interactions clearly demonstrate a reversible control on DNA condensates formation by varying the protamine-to-DNA ratio. Microscopic states and condensate structures occurring in semidilute solutions of short DNA fragments are in good agreement with experimental phase diagram and cryoTEM observations. The reversible microscopic mechanisms induced by protamination modulation should provide valuable information to improve a mechanistic understanding of early and intermediate stages of spermatogenesis where an interplay between condensation and liquid-liquid phase separation triggered by protamine expression and post-translational regulation might occur. Moreover, recent vaccines to prevent virus infections and cancers using protamine as a packaging and depackaging agent might be fine-tuned for improved efficiency using a protamination control.

Stationary mass distribution and nonlocality in models of coalescence and shattering

We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the large and small mass asymptotic behavior of the mass distribution depend on whether the collision kernel is local (the aggregation mass flux is essentially generated by collisions between particles of similar masses) or nonlocal (collision between particles of widely different masses give the main contribution to the mass flux). We show that the nonlocal regime is further divided into two subregimes corresponding to weak and strong nonlocality. We also observe that at the boundaries between the local and nonlocal regimes, the mass distribution acquires logarithmic corrections to scaling and calculate these corrections. Exact solutions for special kernels and numerical simulations are used to validate some nonrigorous steps used in the analysis. Our results show that for local kernels, the scaling solutions carry a constant flux of mass due to aggregation, whereas for the nonlocal case there is a correction to the constant flux exponent. Our results suggest that for general scale-invariant kernels, the universality classes of mass distributions are labeled by two parameters: the homogeneity degree of the kernel and one further number measuring the degree of the nonlocality of the kernel.

Potential of mean force between oppositely charged nanoparticles: A comprehensive comparison between Poisson-Boltzmann theory and Monte Carlo simulations

Ion-mediated interactions between like-charged polyelectrolytes have been paid much attention, and the Poisson-Boltzmann (PB) theory has been shown to fail in qualitatively predicting multivalent ion-mediated like-charge attraction. However, inadequate attention has been paid to the ion-mediated interactions between oppositely charged polyelectrolytes. In this work, the potentials of mean force (PMF) between oppositely charged nanoparticles in 1:1 and 2:2 salt solutions were investigated by Monte Carlo simulations and the PB theory. Our calculations show that the PMFs between oppositely charged nanoparticles are generally attractive in 1:1 and 2:2 salt solutions and that such attractive PMFs become weaker at higher 1:1 or 2:2 salt concentrations. The comprehensive comparisons show that the PB theory can quantitatively predict the PMFs between oppositely charged nanoparticles in 1:1 salt solutions, except for the slight deviation at very high 1:1 salt concentration. However, for 2:2 salt solutions, the PB theory generally overestimates the attractive PMF between oppositely charged nanoparticles, and this overestimation becomes more pronounced for nanoparticles with higher charge density and for higher 2:2 salt concentration. Our microscopic analyses suggest that the overestimation of the PB theory on the attractive PMFs for 2:2 salt solutions is attributed to the underestimation of divalent ions bound to nanoparticles.

Study of the conformation of polyelectrolyte aggregates using coarse-grained molecular dynamics simulations

The conformation of polyelectrolyte aggregates as a function of the backbone rigidity is investigated by coarse-grained molecular dynamics simulation. The polyelectrolyte is represented by a bead-spring chain with charged side chains. The simulations start from the uniform distributions of the polyelectrolytes, and the resultant polyelectrolyte conformation after a few microseconds exhibits spherical self-aggregates, clusters, or bending bundle-like aggregates, depending on the backbone rigidity. The interaggregate structures on a large scale are featured by the static structure factor (SSF). The simulated SSFs of the bending bundle-like aggregates are consistent with those of the small angle X-ray scattering (SAXS) measurement so we successfully assign the microscopic structures of polyelectrolytes to the SAXS measurement. The power-law of the SSFs for the bundle conditions is steeper than that of the conventional cylinder model. The present study finds that such discrepancy in the power-law results from the bending of the bundle-like aggregates. In addition, the relaxation behavior includes slow dynamics. The present study proposes that such slow dynamics results from diffusion-limited aggregation and from gliding processes to reduce local metastable folding within the aggregates.

Unexpected Like-Charge Self-Assembly of a Biguanide-Based Antimicrobial Polyelectrolyte

Polyelectrolyte chains dissolved in good solvent are expected to collapse in compact configurations in the presence of multivalent ions. Here, we show that a weakly charged, hydrophilic polyelectrolyte containing biguanide groups self-assembles in water also in the presence of monovalent counterions, even at low salt concentrations. The polymer assembles in a compact, ordered, hairpin-like shape that, with increasing the ionic strength of the solution, can collapse further in three- or five-folded structures. Neither water nor ions mediate the self-assembly which, instead, is driven by the like-charge pairing of the biguanide units. The thermodynamics of the self-assembly show that the self-association is enthalpically driven, is isodesmic (at least at low aggregation number), and is favored by increasing salt concentration. This unique self-assembly behavior may be linked to the well-known polymer's antimicrobial properties and could help in rationalizing its biological activity.

Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes

We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius R_{g} on the reduced Bjerrum length ℓ_{B} and find two different regimes. In the first one, called a weak electrostatic regime, R_{g}∼ℓ_{B}^{-1/2}, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find R_{g}∼ℓ_{B}^{-1/5}. To explain the novel regime we modify the counterion-fluctuation theory.