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In the context of global gyrokinetic simulations of turbulence using a particle-in-cell framework, verifying the delta-f assumption with a fixed background distribution becomes challenging when determining quasi-steady state profiles corresponding to given sources over long time scales, where plasma profiles can evolve significantly. The advantage of low relative sampling noise afforded by the delta-f scheme is shown to be retained by considering the background as a time-evolving Maxwellian with time-dependent density and temperature profiles. Implementation of this adaptive scheme to simulate electrostatic collisionless flux-driven turbulence in tokamak plasmas show small and nonincreasing sampling noise levels, which would otherwise increase indefinitely with a stationary background scheme. The adaptive scheme furthermore allows one to reach numerically converged results of quasi-steady state with much lower marker numbers. [ABSTRACT FROM AUTHOR]

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation levels are high, for example, in strong gradient regions. For particle-in-cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme makes such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former problem. Under simplified collisionless physics, this adaptive delta-f scheme is shown to reduce noise accumulation in the zonal flows and the simulated heat flux in a quasi-steady turbulent state. The method also avoids the collapse of the signal-to-noise ratio, which occurs in the standard non-adaptive scheme, and, therefore, allows one to reach numerically converged results even with lower marker numbers. [ABSTRACT FROM AUTHOR]

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Electro-osmotic flow (EOF) is a phenomenon where fluid motion occurs in porous materials or micro/nano-channels when an external electric field is applied. In the particular example of single-molecule electrophoresis using single nanopores, the role of EOF on the translocation velocity of the analyte molecule through the nanopore is not fully understood. The complexity arises from a combination of effects from hydrodynamics in restricted environments, electrostatics emanating from charge decorations and geometry of the pores. We address this fundamental issue using the Poisson-Nernst-Planck and Navier-Stokes (PNP-NS) equations for cylindrical solid-state nanopores and three representative protein nanopores (α-hemolysin, MspA, and CsgG). We present the velocity profiles inside the nanopores as a function of charge decoration and geometry of the pore and applied electric field. We report several unexpected results: (a) The apparent charges of the protein nanopores are different from their net charge and the surface charge of the whole protein geometry, and the net charge of inner surface is consistent with the apparent charge. (b) The fluid velocity depends non-monotonically on voltage. The three protein nanopores exhibit unique EOF and velocity-voltage relations, which cannot be simply deduced from their net charge. Furthermore, effective point mutations can significantly change both the direction and the magnitude of EOF. The present computational analysis offers an opportunity to further understand the origins of the speed of transport of charged macromolecules in restricted space and to design desirable nanopores for tuning the speed of macromolecules through nanopores., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We have studied the process of melting of polymer crystals using Langevin dynamics simulations with a coarse-grained united atom model. We have considered two ideal situations: one in which a single crystal melts and the other in which a multichain crystal melts. We show that the melting of the single crystal proceeds through a globular metastable state, which is followed by expansion to a more random coil-like state. Similarly, the melting of the multichain crystal reveals a special mechanism comprising two steps: one in which a long-lived partially molten metastable state is formed, followed by a second step in which the chains peel off from the crystalline core to a free state. We elucidate the nature of the metastable state close to the equilibrium melting temperature and show that the multichain crystals equilibrate to states of intermediate order, with the extent of ordering decreasing as we increase the melting temperature. We quantify the kinetics of melting by estimating a free energy landscape using parallel tempering Langevin dynamics simulations. These simulations reveal a metastable state in the single molecule systems, allowing us to estimate the free energy barriers. Additionally, the melting of the multichain crystals reveals the existence of two barriers, with the preference for the intermediate state reducing with increasing temperature. We compare our findings to the existing experimental evidence and find qualitative agreements.

Polymer crystals grown from melts consist of alternating lamellar crystalline regions and amorphous regions. We study the statistics of ties: chains which bridge the adjacent lamellae, loops: chains which come out of one lamella and enter back into the same lamella before reaching the other lamellae, and tails: chains which end in an amorphous region. We develop a theory to calculate the probabilities of formation of ties, loops, and tails with consideration of finite chain length and cooperative incorporation of a chain into multiple lamellae. The results of our numerical calculations based on a field-theoretic formalism show that the fraction of ties increases with increasing chain length, and it decreases with increasing interlamellar separation. In the limiting case of an infinite chain confined between only two walls, we recover the classical results of the gambler's ruin model. We show that the density anomaly encountered in previous theories is avoided naturally in the present theory without forcing the majority of stems to form tight loops. The derived results on the probability of tie chains in the amorphous regions are pertinent to the mechanical properties of semicrystalline polymers.

This special topic highlights recent advances in experiments, theory, and coarse-grained modeling on charged macromolecular systems involving synthetic and biological polymers and membranes. The behaviors of the charged systems are very complex and are qualitatively different from those of uncharged polymers. The results presented in this special topic provide deep insights into the fundamentals of how the coupling between the long-ranged electrostatic and topological correlations of charged macromolecules controls their conformations, assembly, dynamics, and transport. There are many insights into the creation and design of new materials based on ionic interactions.

We address complex coacervation, the liquid-liquid phase separation of a solution of oppositely charged polyelectrolyte chains into a polyelectrolyte rich complex coacervate phase and a dilute aqueous phase, based on the general premise of spontaneous formation of polycation-polyanion complexes even in the homogeneous phase. The complexes are treated as flexible chains made of dipolar segments and uniformly charged segments. Using a mean field theory that accounts for the entropy of all dissociated ions in the system, electrostatic interactions among dipolar and charged segments of complexes and uncomplexed polyelectrolytes, and polymer-solvent hydrophobicity, we have computed coacervate phase diagrams in terms of polyelectrolyte composition, added salt concentration, and temperature. For moderately hydrophobic polyelectrolytes in water at room temperature, neither hydrophobicity nor electrostatics alone is strong enough to cause phase separation, but their combined effect results in phase separation, arising from the enhancement of effective hydrophobicity by dipolar attractions. The computed phase diagrams capture key experimental observations including the suppression of complex coacervation due to increases in salt concentration, temperature, and polycation-polyanion composition asymmetry, and its promotion by increasing the chain length, and the preferential partitioning of salt into the polyelectrolyte dilute phase. We also provide new predictions such as the emergence of loops of instability with two critical points.

Using light scattering and Atomic Force Microscopy techniques, we have studied the kinetics and equilibrium scattering intensity of collagen association, which is pertinent to the vitreous of the human eye. Specifically, we have characterized fibrillization dependence on pH, temperature, and ionic strength. At higher and lower pH, collagen triple helices remain stable in solution without fibrillization. At physiological pH, fibrillization occurs and the fibril growth is slowed upon either an increase in ionic strength or a decrease in temperature. The total light scattering with respect to ionic strength is non-monotonic in these conditions as a result of a competing dependence of fibril concentration and size on ionic strength. Fibril concentration is the highest at lower ionic strengths and rapidly decays for higher ionic strengths. On the other hand, fibril size is larger in solutions with higher ionic strength. We present a theoretical model, based on dipolar interactions in solutions, to describe the observed electrostatic nature of collagen assembly. At extreme pH values, either very low or very high, collagen triple helices carry a large net charge of the same sign preventing their assembly into fibrils. At intermediate pH values, fluctuations in the charge distribution of the collagen triple helices around roughly zero net charge lead to fibrillization. The growth kinetics of fibrils in this regime can be adequately described by dipolar interactions arising from charge fluctuations.

We have studied the crystallization of ring polymers using Langevin dynamics simulations with a coarse-grained united atom model. We show that there are marked differences in the crystallization of single ring polymers in comparison to single linear polymers. Contrary to expectations from equilibrium thermodynamics, ring polymers melt at lower temperatures than linear polymers. An analysis of the early stage crystallization mechanism shows that ring and linear polymers crystallize through the birth of baby nuclei with their coarsening depending uniquely on their topology. The single ring polymers nucleate faster than the single linear analogs and into several metastable lamellar thicknesses, although the motion of the monomers in both cases is comparable. Additionally, using multiple polymer molecules, we find that the secondary nucleation of ring polymers proceeds with free energy barriers, as opposed to linear polymers where no barriers are found. Our results are in qualitative agreement with some experiments, while in disagreement with some other experiments, indicating additional roles by chemistries of ring and linear polymers. Our simulations are designed to explore only the topological effects without any consideration of non-universal chemical effects for our particular model.

We have measured the rate of capture of single molecules of sodium poly(styrene sulfonate) by α-hemolysin protein pore by varying applied voltage, pH, and the salt concentration asymmetry across the pore. We show that electrostatic interaction between the polyelectrolyte and the protein pore significantly affects the polymer capture rate in addition to the enhancement of drift arising from electrolyte concentration gradient. At higher pH values where the electrostatic interaction between the polymer and the α-hemolysin pore is repulsive, an antagonistic coupling with the drift induced by salt concentration gradient emerges. This antagonistic coupling results in a nonmonotonic dependence of the polymer capture rate on the salt concentration in the donor compartment. The coupling between the pore-polymer interaction and drift can be weakened by increasing the strength of the electric field that drives the polymer translocation. In contrast, at lower pH values where the polymer-pore interaction is attractive, a synergy with the additional drift from salt concentration asymmetry arises and the capture rate depends monotonically on the donor salt concentration. For higher pH, we identify two regimes for the enhancement of capture rate by salt concentration gradient: (a) drift-dominated regime, where the capture rate is roughly quadratic in the ratio of salt concentration in the receiver compartment to that in the donor compartment, and (b) antagonistic coupling regime at higher values of this ratio with a linear relation for the polymer capture rate.

The proteins α-, β-, and γ-crystallins are the major components of the lens in the human eye. Using dynamic light scattering method, we have performed in vitro investigations of protein-protein interactions in dilute solutions of human γ-crystallin and α-crystallin. We find that γ-crystallin spontaneously aggregates into finite-sized clusters in phosphate buffer solutions. There are two distinct populations of unaggregated and aggregated γ-crystallins in these solutions. On the other hand, α-crystallin molecules are not aggregated into large clusters in solutions of α-crystallin alone. When α-crystallin and γ-crystallin are mixed in phosphate buffer solutions, we demonstrate that the clusters of γ-crystallin are prevented. By further investigating the roles of temperature, protein concentration, pH, salt concentration, and a reducing agent, we show that the aggregation of γ-crystallin under our in vitro conditions arises from non-covalent electrostatic interactions. In addition, we show that aggregation of γ-crystallin occurs under the dilute in vitro conditions even in the absence of oxidizing agents that can induce disulfide cross-links, long considered to be responsible for human cataracts. Aggregation of γ-crystallin when maintained under reducing conditions suggests that oxidation does not contribute to the aggregation in dilute solutions.

We present theoretical results on kinetics for the passive wrapping of a single, rigid particle by a flexible membrane. Using a simple geometric ansatz for the shape of the membrane/particle complex we first compute free energy profiles as a function of the particle size, attraction strength between the particle and vesicle, and material properties of the vesicle--bending stiffness and stretching modulus. The free energy profiles thus computed are taken as input to a stochastic model of the wrapping process, described by a Fokker-Planck equation. We compute average uptake rates of the particle into the vesicle. We find that the rate of particle uptake falls to zero outside of a thermodynamically allowed range of particle sizes. Within the thermodynamically allowed range of particle size, the rate of uptake is variable and we compute the optimal particle size and maximal uptake rate as a function of the attraction strength, the vesicle size, and vesicle material properties.

We present results on the sequence dependence of translocation kinetics for a partially charged heteropolymer moving through a very thin pore using theoretical tools and Langevin dynamics simulational techniques. The chain is composed of two types of monomers of differing frictional interaction with the pore and charge. We present exact analytical expressions for passage probability, mean first passage time, and mean successful passage times for both reflecting/absorbing and absorbing/absorbing boundary conditions, showing rich and unexpected dependence of translocation behavior on charge fraction, distribution along the chain, and electric field configuration. We find excellent qualitative and good quantitative agreement between theoretical and simulation results. Surprisingly, there emerges a threshold charge fraction of a diblock copolymer beyond which the success rate of translocation is independent of charge fraction. Also, the mean successful translocation time of a diblock copolymer displays non-monotonic behavior with increasing length of the charged block; there is an optimum length of the charged block where the mean translocation rate is the slowest; and there can be a substantial range of higher charge fractions which make the translocation slower than even a minimally charged chain. Additionally, we find for a fixed total charge on the chain, finer distribution along the backbone significantly decreases mean translocation time.

The molecular mechanisms guiding the self-assembly of proteins into functional or pathogenic large-scale structures can be only understood by studying the correlation between the structural details of the monomer and the eventual mesoscopic morphologies. Among the myriad structural details of protein monomers and their manifestations in the self-assembled morphologies, we seek to identify the most crucial set of structural features necessary for the spontaneous selection of desired morphologies. Using a combination of the structural information and a Monte Carlo method with a coarse-grained model, we have studied the functional protein self-assembly into S(surface)-layers, which constitute the crystallized outer most cell envelope of a great variety of bacterial cells. We discover that only few and mainly hydrophobic amino acids, located on the surface of the monomer, are responsible for the formation of a highly ordered anisotropic protein lattice. The coarse-grained model presented here reproduces accurately many experimentally observed features including the pore formation, chemical description of the pore structure, location of specific amino acid residues at the protein-protein interfaces, and surface accessibility of specific amino acid residues. In addition to elucidating the molecular mechanisms and explaining experimental findings in the S-layer assembly, the present work offers a tool, which is chemical enough to capture details of primary sequences and coarse-grained enough to explore morphological structures with thousands of protein monomers, to promulgate design rules for spontaneous formation of specific protein assemblies.

Single polymer chains under spatially heterogeneous confinement are investigated through simulation of a chain in an infinite linear series of chambers and pores. Conformational properties studied include the number of occupied chambers and the radius of gyration along the chamber axis, both of which vary with chain length and chamber size according to simple scaling predictions. The probability distribution of chain spatial extent along the chamber axis is characterized by distinct peaks and troughs corresponding to favored and disfavored chain sizes. The large scale dynamics is characterized by the center-of-mass diffusion constant along the chamber axis, which exhibits an exponential dependence on chamber size with dramatically slower diffusion in larger chambers. Stepping time distributions change as the chamber size increases or chain length decreases from a symmetric form to a Poisson distribution. The evolution of the dynamics is suggestive of a substantial barrier, independent of chain length, that controls the large-scale motion for short-enough chains in large-enough chambers. Other known signatures of anomalous, nondiffusive dynamics are also observed. The onset of barrier-controlled or anomalous dynamics is conjectured to be the result of chains occupying only a small number of chambers simultaneously.

We have computed the phase diagrams of solutions of flexible polyelectrolyte chains with added simple electrolytes. The calculations are based on our recent theory [M. Muthukumar, Macromolecules 35, 9142 (2002)], which accounts for conformational fluctuations of chains, charge density correlations arising from dissolved ions, hydrophobic interaction between polymer backbone and solvent, and translational entropy of all species in the system. The theory is at the mean field level and recovers the results of the restricted primitive model with the Debye-Huckel description for solutions of simple electrolytes without any polymer chains and those of the Flory-Huggins and scaling theories for uncharged polymers in the absence of charges or electrolytes. In constructing the phase diagrams, the chemical potential of each of the species is maintained to be the same in the coexisting phases and at the same time each phase being electrically neutral (Donnan equilibrium). Comparisons are made with a more constrained situation where the chemical potentials of the independent components are maintained to be the same in the coexisting phases. Our calculations predict several rich phenomena. Even for the salt-free solutions, two critical phenomena (corresponding to the Flory-Huggins-type and the restricted-primitive-model-type critical points) are predicted. The coupling between these two leads to two critical end points and triple points. In the presence of salt, the valency of electrolyte ions is found to influence drastically the phase diagrams. Specifically, the predicted liquid-liquid phase transitions in certain temperature ranges is reminiscent of the re-entrant-precipitation phenomenon observed experimentally for polyelectrolytes condensed with trivalent salts.