Influence of temperature on bend, twist and twist-bend coupling of dsDNA.

The temperature-dependent bend and twist elasticities of dsDNA, as well as their couplings, were explored through all-atom molecular dynamics simulations. Three rotational parameters, tilt, roll, and twist, were employed to assess the bend and twist elasticities through their stiffness matrix. Our analysis indicates that the bend and twist stiffnesses decrease as the temperature rises, primarily owing to entropic influences stemming from thermodynamic fluctuations. Furthermore, the couplings between these rotational parameters also exhibit a decline with increasing temperature, although the roll-twist coupling displays greater strength than the tilt-roll and tilt-twist couplings, attributed to its more robust correction component. We elucidated the influence of temperature on bend and twist elasticities based on the comparisons between various models and existing data.

Mechanical response of double-stranded DNA: Bend, twist, and overwind.

We employed all-atom molecular dynamics simulations to explore the mechanical response of bending, twisting, and overwinding for double-stranded DNA (dsDNA). We analyzed the bending and twisting deformations, as well as their stiffnesses, using the tilt, roll, and twist modes under stretching force. Findings indicate that the roll and twist angles vary linearly with the stretching force but show opposite trends. The tilt, roll, and twist elastic moduli are considered constants, while the coupling between roll and twist modes slightly decreases under stretching force. The effect of the stretching force on the roll and twist modes, including both their deformations and elasticities, exhibits sequence-dependence, with symmetry around the base pair step. Furthermore, we examined the overwinding path and mechanism of dsDNA from the perspective of the stiffness matrix, based on the tilt, roll, and twist modes. The correlations among tilt, roll, and twist angles imply an alternative overwinding pathway via twist-roll coupling when dsDNA is stretched, wherein entropic contribution prevails.

Temperature dependence of DNA elasticity: An all-atom molecular dynamics simulation study.

We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist-stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist-stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study.

The interaction between macromolecular chains and phospholipid membranes in aqueous solution was investigated using dissipative particle dynamics simulations. Two cases were considered, one in which the macromolecular chains were pulled along parallel to the membrane surfaces and another in which they were pulled vertical to the membrane surfaces. Several parameters, including the radius of gyration, shape factor, particle number, and order parameter, were used to investigate the interaction mechanisms during the dynamics processes by adjusting the pulling force strength of the chains. In both cases, the results showed that the macromolecular chains undergo conformational transitions from a coiled to a rod-like structure. Furthermore, the simulations revealed that the membranes can be damaged and repaired during the dynamic processes. The role of the pulling forces and the adsorption interactions between the chains and membranes differed in the parallel and perpendicular pulling cases. These findings contribute to our understanding of the interaction mechanisms between macromolecules and membranes, and they may have potential applications in biology and medicine.

A Machine Learning Model to Classify Dynamic Processes in Liquid Water.

The dynamics of water molecules plays a vital role in understanding water. We combined computer simulation and deep learning to study the dynamics of H-bonds between water molecules. Based on ab initio molecular dynamics simulations and a newly defined directed Hydrogen (H-) bond population operator, we studied a typical dynamic process in bulk water: interchange, in which the H-bond donor reverses roles with the acceptor. By designing a recurrent neural network-based model, we have successfully classified the interchange and breakage processes in water. We have found that the ratio between them is approximately 1 : 4, and it hardly depends on temperatures from 280 to 360 K. This work implies that deep learning has the great potential to help distinguish complex dynamic processes containing H-bonds in other systems.

Neural network model for structure factor of polymer systems.

As an important physical quantity to understand the internal structure of polymer chains, the structure factor is being studied both in theory and experiment. Theoretically, the structure factor of Gaussian chains has been solved analytically, but for wormlike chains, numerical approaches are often used, such as Monte Carlo simulations, solving the modified diffusion equation. In these works, the structure factor needs to be calculated differently for different regions of the wave vector and chain rigidity, and some calculation processes are resource consuming. In this work, by training a deep neural network, we obtained an efficient model to calculate the structure factor of polymer chains, without considering different regions of wavenumber and chain rigidity. Furthermore, based on the trained neural network model, we predicted the contour and Kuhn lengths of some polymer chains by using scattering experimental data, and we found that our model can get pretty reasonable predictions. This work provides a method to obtain the structure factor for polymer chains, which is as good as previous and more computationally efficient. It also provides a potential way for the experimental researchers to measure the contour and Kuhn lengths of polymer chains.

Self-assembly of phospholipid molecules in solutions under shear flows: Microstructures and phase diagrams.

Shear-induced microstructures and their phase diagrams were investigated for phospholipid molecules in aqueous solution by dissipative particle dynamic simulation. Self-assembled microstructures, including spherical and cylindrical micelles, spherical vesicles, lamellae, undulated lamellae, perforated lamellae, and continuous networks, were observed under various shear flows and phospholipid concentrations, where the spatial inhomogeneity and symmetry were analysed. A series of phase diagrams were constructed based on the chain lengths under various phospholipid concentrations. The phase distributions showed that the structures with spherical symmetry could be shear-induced to structures with cylindrical symmetry in the dilute solutions. In the semi-concentrated solutions, the lamellae were located in most spaces under zero shear flows, which could be shear-induced into undulated lamellae and then into cylindrical micelles. For the concentrated solutions, the strong shear flows oriented the directions of multilayer lamellae and phase transitions appeared between several cylindrical network structures. These observations on shear-induced microstructures and their distributions revealed a promising approach that could be used to design bio-microstructures based on phospholipid molecules under shear flows.

Perspective: parameters in a self-consistent field theory of multicomponent wormlike-copolymer melts.

We review a formalism that can be used to calculate the microphase-separated crystallographic structures of multi-component wormlike polymer melts. The approach is based on a self-consistent field theory of wormlike polymers where the persistence length of each component is an important parameter. We emphasize on an analysis of the number of independent parameters required to specify a problem in general, for a system that includes Flory-Huggins and Maier-Saupe energies. Examples of recent applications are also briefly demonstrated: AB homopolymer interface, AB diblock copolymers, and rod-coil copolymers.

Phase diagrams of diblock copolymers in electric fields: a self-consistent field theory study.

We investigated the phase diagrams of diblock copolymers in external electrostatic fields by using real-space self-consistent field theory. The lamella, cylinder, sphere, and ellipsoid structures were observed and analyzed by their segment distributions, which were arranged to two types of phase diagrams to examine the phase behavior in weak and strong electric fields. One type was constructed on the basis of Flory-Huggins interaction parameter and volume fraction. We identified an ellipsoid structure with a body-centered cuboid arrangement as a stable phase and discussed the shift of phase boundaries in the electric fields. The other type of phase diagrams was established on the basis of the dielectric constants of two blocks in the electric fields. We then determined the regions of ellipsoid phase in the phase diagrams to examine the influence of dielectric constants on the phase transition between ellipsoidal and hexagonally packed cylinder phases. A general agreement was obtained by comparing our results with those described in previous experimental and theoretical studies.

Complex liquid-crystal nanostructures in semiflexible ABC linear triblock copolymers: A self-consistent field theory.

We show that two series of ABC linear triblock copolymers possess sequences of order-to-order phase transitions between microphase-separated states, as the degree of flexibility of the semiflexible middle B-blocks varies. The spatial and orientational symmetries of these phases, some of them containing liquid-crystal ordering, are analysed in comparison with related structures previously determined experimentally and theoretically. A theoretical framework based on the self-consistent field treatment of the wormlike-chain model, which incorporates the Flory-Huggins and Maier-Saupe interactions in the free energy, is used here as a basic foundation for numerical calculations. We suggest that tuning the flexibility parameter, which reduces to the concept of degree of polymerization in the coil-like limit and characterizes the chain-persistency in the rod-like limit, provides a promising approach that can be used to design the resulting microphase-separated structures in semiflexible copolymer melts.

Phase transitions in semiflexible-rod diblock copolymers: a self-consistent field theory.

We investigate the phase behavior of semiflexible-rod diblock copolymers in a parameter range where the system displays columnar and lamella structures, using a self-consistent field theory based on the wormlike-chain model. Both Flory-Huggins and Maier-Saupe orientational interactions are incorporated in the formalism, which allows us to explore microphase separation and liquid-crystal ordering simultaneously. Order-to-order phase transitions induced by chain rigidity and orientational interaction are both reported and analyzed. Coupled orientational ordering and spatial inhomogeneity of the four microphase-separated states are discussed in this work: hexagonal column, ellipse column, smectic-A, and smectic-C.

Self-Assembly of Lipid Molecules under Shear Flows: A Dissipative Particle Dynamics Simulation Study.

The self-assembly of lipid molecules in aqueous solution under shear flows was investigated using the dissipative particle dynamics simulation method. Three cases were considered: zero shear flow, weak shear flow and strong shear flow. Various self-assembled structures, such as double layers, perforated double layers, hierarchical discs, micelles, and vesicles, were observed. The self-assembly behavior was investigated in equilibrium by constructing phase diagrams based on chain lengths. Results showed the remarkable influence of chain length, shear flow and solution concentration on the self-assembly process. Furthermore, the self-assembly behavior of lipid molecules was analyzed using the system energy, particle number and shape factor during the dynamic processes, where the self-assembly pathways were observed and analyzed for the typical structures. The results enhance our understanding of biomacromolecule self-assembly in a solution and hold the potential for applications in biomedicine.

A physics-informed neural network based on mixed data sampling for solving modified diffusion equations.

We developed a physics-informed neural network based on a mixture of Cartesian grid sampling and Latin hypercube sampling to solve forward and backward modified diffusion equations. We optimized the parameters in the neural networks and the mixed data sampling by considering the squeeze boundary condition and the mixture coefficient, respectively. Then, we used a given modified diffusion equation as an example to demonstrate the efficiency of the neural network solver for forward and backward problems. The neural network results were compared with the numerical solutions, and good agreement with high accuracy was observed. This neural network solver can be generalized to other partial differential equations.

Dynamic Processes and Mechanical Properties of Lipid-Nanoparticle Mixtures.

In this study, we investigate the dynamic processes and mechanical properties of lipid nanoparticle mixtures in a melt via dissipation particle dynamic simulation. By investigating the distribution of nanoparticles in lamellar and hexagonal lipid matrices in equilibrium state and dynamic processes, we observe that the morphology of such composites depends not only on the geometric features of the lipid matrix but also on the concentration of nanoparticles. The dynamic processes are also demonstrated by calculating the average radius of gyration, which indicates the isotropic conformation of lipid molecules in the x-y plane and that the lipid chains are stretched in the z direction with the addition of nanoparticles. Meanwhile, we predict the mechanical properties of lipid-nanoparticle mixtures in lamellar structures by analyzing the interfacial tensions. Results show that the interfacial tension decreased with the increase in nanoparticle concentration. These results provide molecular-level information for the rational and a priori design of new lipid nanocomposites with ad hoc tailored properties.

Nanostructures and phase diagrams of ABC star triblock copolymers in pore geometries.

The nanostructures and phase diagrams of ABC star triblock copolymers in pore geometries are investigated using the real-space self-consistent field theory in two-dimensional space. Two types of pores with neutral surfaces, namely, pores with small and large diameters, are considered. A rich variety of nanostructures are exhibited by the ABC star triblock copolymers in these two types of pores, which differ from those observed in bulk and in other confinements. These structures include perpendicular undulating lamellae, concentric core-shell cylinders, polygonal tiling with cylindrical arrangements, and other complex structures. Triangular phase diagrams for the ABC star triblock copolymers are constructed. The small pores clearly affect the corner and central space of the phase diagrams by distorting the bulk structures into concentric arrangements. Meanwhile, the large pores induce the transformation of bulk structures into concentric structures in most of the phase space, but slightly affect the structures at the center of the phase diagrams. Furthermore, the order-order and order-disorder phase transitions, as well as the stable and metastable phases, in the triangular phase diagrams are examined by analyzing their free energies. These observations on the ABC star triblock copolymers in the pore geometries provide a deeper insight into the behavior of macromolecules in a confined system.

Self-Assembly of Lipid Mixtures in Solutions: Structures, Dynamics Processes and Mechanical Properties.

The self-assembly of lipid mixtures in aqueous solution was investigated by dissipative particle dynamics simulation. Two types of lipid molecules were modelled, where three mixed structures, i.e., the membrane, perforated membrane and vesicle, were determined in the self-assembly processes. Phase behaviour was investigated by using the phase diagrams based on the tail chain lengths for the two types of lipids. Several parameters, such as chain number and average radius of gyration, were employed to explore the structural formations of the membrane and perforated membrane in the dynamic processes. Interface tension was used to demonstrate the mechanical properties of the membrane and perforated membrane in the equilibrium state and dynamics processes. Results help us to understand the self-assembly mechanism of the biomolecule mixtures, which has a potential application for designing the lipid molecule-based bio-membranes in solutions.

Geometric frustration phases of diblock copolymers in nanoparticles.

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.

Role of polyunsaturated phospholipids in liquid-ordered and liquid-disordered phases.

Polyunsaturated phospholipids interact complexly with other membrane components. We have examined pair interactions among ternary lipid bilayers composed of saturated DPPC, polyunsaturated PLePC, and cholesterol in the liquid-ordered and the liquid-disordered phases by all-atom molecular dynamics simulations. The results show that PLePC exhibits strong repulsion with DPPC and cholesterol in the liquid-disordered phase. When the bilayer changes to the liquid-ordered phase, the repulsion of PLePC with DPPC and cholesterol reduces significantly. The phase state of the bilayer which affects the order of acyl tails as well as their density distributions along the bilayer normal is a key factor regulating the role of PLePC in lipid mixtures. Polyunsaturated phospholipids play a strong repulsive role in the liquid-disordered phase but a weak role in the liquid-ordered phase.

Asymmetric Lipid Membranes under Shear Flows: A Dissipative Particle Dynamics Study.

We investigate the phase behavior of the asymmetric lipid membranes under shear flows, using the dissipative particle dynamics simulation. Two cases, the weak and strong shear flows, are considered for the asymmetric lipid microstructures. Three typical asymmetric structures, the membranes, tubes, and vesicle, are included in the phase diagrams, where the effect of two different types of lipid chain length on the formation of asymmetric membranes is evaluated. The dynamic processes are demonstrated for the asymmetric membranes by calculating the average radius of gyration and shape factor. The result indicates that different shear flows will affect the shape of the second type of lipid molecules; the shape of the first type of lipid molecules is more stable than that of the second type of lipid molecules. The mechanical properties are investigated for the asymmetric membranes by analyzing the interface tension. The results reveal an absolute pressure at the junctions of different types of particles under the weak shear flow; the other positions are almost in a state of no pressure; there is almost no pressure inside the asymmetric lipid membrane structure under the strong shear flow. The findings will help us to understand the potential applications of asymmetric lipid microstructures in the biological and medical fields.

Translocation of α-helix chains through a nanopore.

The translocation of α-helix chains through a nanopore is studied through Langevin dynamics simulations. The α-helix chains exhibit several different characteristics about their average translocation times and the α-helix structures when they transport through the nanopores under the driving forces. First, the relationship between average translocation times τ and the chain length N satisfies the scaling law, τ∼N(α), and the scaling exponent α depends on the driving force f for the small forces while it is close to the Flory exponent (ν) in the other force regions. For the chains with given chain lengths, it is observed that the dependence of the average translocation times can be expressed as τ∼f(-1/2) for the small forces while can be described as τ∼f in the large force regions. Second, for the large driving force, the average number of α-helix structures N(h) decreases first and then increases in the translocation process. The average waiting time of each bead, especially of the first bead, is also dependent on the driving forces. Furthermore, an elasticity spring model is presented to reasonably explain the change of the α-helix number during the translocation and its elasticity can be locally damaged by the large driving forces. Our results demonstrate the unique behaviors of α-helix chains transporting through the pores, which can enrich our insights into and knowledge on biopolymers transporting through membranes.