Atomistic simulations of liquid crystal mixtures of alkoxy substituted phenylpyrimidines 2PhP and PhP14.

We study liquid crystal mixtures of alkoxy substituted phenylpyrimidines 2-[4-(butyloxy)phenyl]-5-(octyloxy)pyrimidine (2PhP) and 2-[4-(tetradecyloxy)phenyl]-5-(tetradecyloxy)pyrimidine (PhP14) using molecular dynamics simulations at the all atom level. The molecular length of PhP14 is 1.8 times that of 2PhP, resulting in an interesting binary mixture phase diagram. Our simulations are composed of 1000-1600 molecules for a total of 80,000-130,000 atomic sites, with total simulation times of 60-100 ns. We first show that a pure 2PhP system self-assembles into isotropic, nematic, smectic A and smectic C phases, and a pure PhP14 system self-assembles into isotropic and smectic C phases. Binary mixtures of PhP14 and 2PhP display a stabilization of the smectic A phase at the expense of the smectic C and nematic phases. We determine that the concentration-induced phase transition from the smectic C to the smectic A phase in the mixture is driven by an out-of-layer fluctuation arrangement of the molecules. We also observe that the tilt angle in the smectic C phases formed in the mixtures is concentration dependent. The results of our simulations are in good agreement with the experimental findings of Kapernaum et al. [J. Org. Chem. 5, 65 (2009)], thus showing that atomistic simulations are capable of reproducing the phase behavior of liquid crystal mixtures and can also provide microscopic details regarding the mechanisms that govern phase stability.

Solvent-shift Monte Carlo: a cluster algorithm for solvated systems.

We present a cluster algorithm for the efficient simulation of solvated systems that we term solvent-shift Monte Carlo (SSMC). The algorithm involves a conformational change in a solvated solute molecule of interest, followed by a concerted movement of solvent particles about a rotation axis. The method satisfies detailed balance and can be applied to existing schemes to sample conformational space, where an axis or plane of rotation can be defined. We demonstrate that the algorithm significantly enhances the sampling of phase space in solvated systems, and may be easily combined with other advanced sampling techniques.

Self-assembled chiral superstructures composed of rigid achiral molecules and molecular scale chiral induction by dopants.

We explore the phase behavior of a rigid achiral bent-core model system. Nematic and smectic phases form at higher densities, whereas micelles and columns composed of chiral clusters of these molecules self-assemble at lower densities. No nucleation mechanism requiring transient chirality is possible in the formation of these chiral superstructures due to the rigid achiral nature of the substituents. We show the chiral micelles are minima of the potential energy surface using energy minimization and parallel tempering simulations. Chiral dopants were found to induce the system to adopt a consistent chiral twist direction, the first molecular scale computer simulation of this effect.

Monte Carlo simulations.

A description of Monte Carlo methods for simulation of proteins is given. Advantages and disadvantages of the Monte Carlo approach are presented. The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented. Some of the standard and some of the more recent ways of performing Monte Carlo on proteins are presented. A discussion of the estimation of errors in properties calculated by Monte Carlo is given.

Modeling microscopic swimmers at low Reynolds number.

The authors employ three numerical methods to explore the motion of low Reynolds number swimmers, modeling the hydrodynamic interactions by means of the Oseen tensor approximation, lattice Boltzmann simulations, and multiparticle collision dynamics. By applying the methods to a three bead linear swimmer, for which exact results are known, the authors are able to compare and assess the effectiveness of the different approaches. They then propose a new class of low Reynolds number swimmers, generalized three bead swimmers that can change both the length of their arms and the angle between them. Hence they suggest a design for a microstructure capable of moving in three dimensions. They discuss multiple bead, linear microstructures and show that they are highly efficient swimmers. They then turn to consider the swimming motion of elastic filaments. Using multiparticle collision dynamics the authors show that a driven filament behaves in a qualitatively similar way to the micron-scale swimming device recently demonstrated by Dreyfus et al. [Nature (London) 437, 862 (2005)].

Quantifying influenza vaccine efficacy and antigenic distance.

We introduce a new measure of antigenic distance between influenza A vaccine and circulating strains. The measure correlates well with efficacies of the H3N2 influenza A component of the annual vaccine between 1971 and 2004, as do results of a theory of the immune response to influenza following vaccination. This new measure of antigenic distance is correlated with vaccine efficacy to a greater degree than are current state of the art phylogenetic sequence analyses or ferret antisera inhibition assays. We suggest that this new measure of antigenic distance be used in the design of the annual influenza vaccine and in the interpretation of vaccine efficacy monitoring.

Glassy dynamics in the adaptive immune response prevents autoimmune disease.

The immune system normally protects the human host against death by infection. However, when an immune response is mistakenly directed at self-antigens, autoimmune disease can occur. We describe a model of protein evolution to simulate the dynamics of the adaptive immune response to antigens. Computer simulations of the dynamics of antibody evolution show that different evolutionary mechanisms, namely, gene segment swapping and point mutation, lead to different evolved antibody binding affinities. Although a combination of gene segment swapping and point mutation can yield a greater affinity to a specific antigen than point mutation alone, the antibodies so evolved are highly cross reactive and would cause autoimmune disease, and this is not the chosen dynamics of the immune system. We suggest that in the immune system's search for antibodies, a balance has evolved between binding affinity and specificity.

Induced and spontaneous deracemization in bent-core liquid crystal phases and in other phases doped with bent-core molecules.

Recently discovered chiral properties of several bent-core smectic liquid crystal phases are summarized and discussed in detail under the assumption that typical bent-core molecules may exist in chiral conformational states and are achiral only on average. Results of atomistic computer simulations are presented which indicate the existence of strongly chiral conformational states for typical bent-core mesogens. A theory is developed which describes a possible shift of equilibrium between left- and right-handed conformations in a macroscopically chiral phase. The theory describes a chirality induction in the B2 bent-core phase and a reduction of the helical pitch in cholesteric and chiral SmC* phases doped with bent-core molecules. Finally, the possibility of spontaneous deracemization in bent-core smectic phases is discussed in detail.

Markov chains of infinite order and asymptotic satisfaction of balance: application to the adaptive integration method.

Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.

Parallel tempering: theory, applications, and new perspectives.

We review the history of the parallel tempering simulation method. From its origins in data analysis, the parallel tempering method has become a standard workhorse of physicochemical simulations. We discuss the theory behind the method and its various generalizations. We mention a selected set of the many applications that have become possible with the introduction of parallel tempering, and we suggest several promising avenues for future research.

Evolvability is a selectable trait.

Concomitant with the evolution of biological diversity must have been the evolution of mechanisms that facilitate evolution, because of the essentially infinite complexity of protein sequence space. We describe how evolvability can be an object of Darwinian selection, emphasizing the collective nature of the process. We quantify our theory with computer simulations of protein evolution. These simulations demonstrate that rapid or dramatic environmental change leads to selection for greater evolvability. The selective pressure for large-scale genetic moves such as DNA exchange becomes increasingly strong as the environmental conditions become more uncertain. Our results demonstrate that evolvability is a selectable trait and allow for the explanation of a large body of experimental results.

Calculations of helical twisting powers from intermolecular torques.

We present a Monte Carlo molecular simulation method that calculates the helical twisting power of a chiral molecule by sampling intermolecular torques. The approach is applied to an achiral nematic liquid crystalline system, composed of Gay-Berne particles, that is doped with chiral molecules. Calculations are presented for six chiral dopant molecules and the results show a good correlation with the sign and magnitude of experimentally determined helical twisting powers.