Minimal Coarse-Grained Model for Immunoglobulin G: Diffusion and Binding under Crowding.

Immunoglobulin G (IgG) is the most common type of antibody found in blood and extracellular fluids and plays an essential role in our immune response. However, studies of the dynamics and reaction kinetics of IgG-antigen binding under physiological crowding conditions are scarce. Herein, we develop a coarse-grained model of IgG consisting of only six beads that we find minimal for a coarse representation of IgG's shape and a decent reproduction of its flexibility and diffusion properties measured experimentally. Using this model in Brownian dynamics simulations, we find that macromolecular crowding affects only slightly the IgG's flexibility, as described by the distribution of angles between the IgG's arms and stem. Our simulations indicate that, contrary to expectations, crowders slow down the translational diffusion of an IgG less strongly than they do for a smaller Ficoll 70, which we relate to the IgG's conformational size changes induced by crowding. We also find that crowders affect the binding kinetics by decreasing the rate of the first binding step and enhancing the second binding step.

How macromolecules softness affects diffusion under crowding.

Diffusion in a macromolecularly crowded environment is essential for many intracellular processes, from metabolism and catalysis to gene transcription and translation. So far, theoretical and experimental work has focused on anomalous subdiffusion, and the effects of interactions, shapes, and composition, while the compactness or softness of macromolecules has received less attention. Herein, we use Brownian dynamics simulations to study how the softness of crowders affects macromolecular diffusion. We find that in most cases, soft crowders slow down the diffusion less effectively than hard crowders like Ficoll. For instance, at a 30% occupied volume fraction, the diffusion in Ficoll70 is about 20% slower than in soft crowders of the same size. However, our simulations indicate that elongated macromolecules, such as double-stranded DNA pieces, can diffuse comparably or even faster in hard crowders. We relate these effects to the volume excluded by soft and hard crowders to different tracers. Our results show that the softness and shape of macromolecules are crucial factors determining diffusion under crowding, relevant to diverse intracellular environments.

Simulations of the 2D self-assembly of tripod-shaped building blocks.

We introduce a molecular dynamics (MD) coarse-grained model for the description of tripod building blocks. This model has been used by us already for linear, V-shape, and tetratopic molecules. We wanted to further extend its possibilities to trifunctional molecules to prove its versatility. For the chosen systems we have also compared the MD results with Monte Carlo results on a triangular lattice. We have shown that the constraints present in the latter method can enforce the formation of completely different structures, not reproducible with off-lattice simulations. In addition to that, we have characterized the obtained structures regarding various parameters such as theoretical diffraction pattern and average association number.

Microscopic density functional theory for monolayers of diblock copolymers.

We propose density functional theory for diblock copolymers in two dimensions. Our theoretical framework is based on Wertheim's first order thermodynamic perturbation theory. Using the proposed approach, we investigate the structure and phase behavior of monolayers of symmetric diblock copolymers. We find that the phase behavior of symmetric diblock copolymer monolayers is similar to that in 3D. This includes the scaling of the equilibrium lamellar width with chain length. We find that the topology of the resulting phase diagrams depends on the chain length and the unlike segment interaction incompatibility and involves either one, two, or three triple points (one of them being the peritectic point). We expect that a similar phase behavior could be obtained for monolayers of colloidal suspensions with carefully tuned interparticle interactions.

Two-dimensional binary mixtures of patchy particles and spherical colloids.

Using Monte Carlo simulation we study two dimensional mixtures of patchy and spherically symmetric particles. Such mixtures can be synthesized experimentally by covering colloids with appropriate types of DNA strands [L. Feng, et al., Adv. Mater., 2013, 25, 2779]. We focus on finding out the ordered structures that can be formed in such systems. The type of ordered phase strongly depends on the valency, size and binding energy of the patchy particles. If the patch size is small enough, i.e. it allows only one spherically symmetric particle to be bound, the ordered structure follows either a hexagonal or a tetragonal pattern depending on the valency of the patchy particles. Moreover, we find stable quasicrystals of dodecagonal symmetry. Additional structures can be obtained if the patches are larger and the binding energy is higher. Depending on the valency of the patchy particles we find either lanes or branched structures forming polygons of the spherically symmetric particles with few patchy particles inside. For pentavalent patchy particles we find stable quasicrystals of decagonal symmetry.

Density functional theory for polymeric systems in 2D.

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

Structure and phase behaviour of diblock copolymer monolayers investigated by means of Monte Carlo simulation.

We use grand canonical Monte Carlo simulation paired with multiple histogram reweighting, hyperparallel tempering and finite size scaling to investigate the structure and phase behaviour of monolayers of diblock copolymers. The chain molecules are arranged on the square lattice and we consider both fully flexible and rod-coil polymer models. In contrast to the majority of previous studies we assume that the interactions between the segments belonging to one of the two subunits are weaker than the remaining segment-segment interactions. We find that when the diblock copolymer is fully flexible, this choice of the interactions leads to a suppression of the ordered phase, and the phase behaviour is analogous to that of the fully flexible homopolymer model. However, when one of the subunits is rigid, we observe the formation of a novel hairpin chessboard ordered structure with fully stretched chains bent in the middle. The topology of the phase diagram depends on the chain length. For shorter chains the global phase diagram features a critical point and a triple point. For longer chains the gas-disordered liquid phase transition is suppressed and only the order-disorder transition remains stable. The resulting phase diagram is of the swan neck type.

Adsorption of block copolymers on solid surfaces: A Monte Carlo study.

Using hyper-parallel tempering Monte Carlo simulation, multiple histogram reweighting method, and finite size scaling, we investigate the adsorption of fully flexible and rod-coil chains on the square lattice. We find that the phase behaviour changes with the chain length and flexibility. For homonuclear rod-coil chains, the phase diagram consists of only gas-disorder liquid critical point. Weakening of the interaction energy between the segments belonging to two different subunits gives rise to an order-disorder transition. The topology of the resulting phase diagram depends on the chain length and flexibility. For short chains, both fully flexible and rod-coil diblock copolymers form lamellar ordered phase with fully stretched chains, and the order-disorder transition is of the first order. The phase diagrams are similar for both chain architectures and consist of two binodals meeting in the triple point. When the chain length increases the order-disorder transition becomes second-order and the difference in the phase behaviour between the fully flexible and the rod-coil diblock copolymers becomes more pronounced. While for the former chain architecture the topology of the phase diagram involves a λ-line which meets the gas-disordered liquid binodal in the critical end-point, in the latter case the λ-line meets the gas-disordered liquid critical point and forms the tricritical point. We trace back these changes to the change in the morphology of the ordered phase. The mechanism of the order-disorder transition involves the formation of domains resembling those observed during the spinodal decomposition process. The domains subsequently merge and arrange into lamellae. These observations are supported by integral geometry analysis.