Michael Nayhouse

Modeling the Self-Assembly of Lipids and Nanotubes in Solution: Forming Vesicles and Bicelles with Transmembrane Nanotube Channels

Via dissipative particle dynamics (DPD), we simulate the self-assembly of end-functionalized, amphiphilic nanotubes and lipids in a hydrophilic solvent. Each nanotube encompasses a hydrophobic stalk and two hydrophilic ends, which are functionalized with end-tethered chains. With a relatively low number of the nanotubes in solution, the components self-assemble into stable lipid-nanotube vesicles. As the number of nanotubes is increased, the system exhibits a vesicle-to-bicelle transition, resulting in stable hybrid bicelle. Moreover, our results reveal that the nanotubes cluster into distinct tripod-like structures within the vesicles and aggregate into a ring-like assembly within the bicelles. For both the vesicles and bicelles, the nanotubes assume trans-membrane orientations, with the tethered hairs extending into the surrounding solution or the encapsulated fluid. Thus, the hairs provide a means of regulating the transport of species through the self-assembled structures. Our findings provide guidelines for creating nanotube clusters with distinctive morphologies that might be difficult to achieve through more conventional means. The results also yield design rules for creating synthetic cell-like objects or microreactors that can exhibit biomimetic functionality.

Selected AB42−/− (A = C, Si, Ge; B = Al, Ga, In) ions: a battle between covalency and aromaticity, and prediction of square planar Si in SiIn42−/−

CAl(4)(2-/-) (D(4h), (1)A(1g)) is a cluster ion that has been established to be planar, aromatic, and contain a tetracoordinate planar C atom. Valence isoelectronic substitution of C with Si and Ge in this cluster leads to a radical change of structure toward distorted pentagonal species. We find that this structural change goes together with the cluster acquiring partial covalency of bonding between Si/Ge and Al(4), facilitated by hybridization of the atomic orbitals (AOs). Counter intuitively, for the AAl(4)(2-/-) (A = C, Si, Ge) clusters, hybridization in the dopant atom is strengthened from C, to Si, and to Ge, even though typically AOs are more likely to hybridize if they are closer in energy (i.e. in earlier elements in the Periodic Table). The trend is explained by the better overlap of the hybrids of the heavier dopants with the orbitals of Al(4). From the thus understood trend, it is inferred that covalency in such clusters can be switched off, by varying the relative sizes of the AOs of the main element and the dopant. Using this mechanism, we then successfully killed covalency in Si, and predicted a new aromatic cluster ion containing a tetracoordinate square planar Si, SiIn(4)(2-/-).

A Monte Carlo study of the freezing transition of hard spheres

A simulation method for fluid-solid transitions, which is based on a modification of the constrained cell model of Hoover and Ree, is developed and tested on a system of hard spheres. In the fully occupied constrained cell model, each particle is confined in its own Wigner-Seitz cell. Constant-pressure simulations of the constrained cell model for a system of hard spheres indicate a point of mechanical instability at a density which is about 64% of the density at the close packed limit. Below that point, the solid is mechanically unstable since without the confinement imposed by the cell walls it will disintegrate to a disordered, fluid-like phase. Hoover and Ree proposed a modified cell model by introducing an external field of variable strength. High values of the external field variable favor configurations with one particle per cell and thus stabilize the solid phase. In this work, the modified cell model of a hard-sphere system is simulated under constant-pressure conditions using tempering and histogram reweighting techniques. The simulations indicate that as the strength of the field is reduced, the transition from the solid to the fluid phase is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the hard-sphere system is determined by analyzing the field-induced fluid-solid transition of the modified cell model in the limit in which the external field vanishes. The coexistence pressure and densities are obtained through finite-size scaling techniques and are in good accord with previous estimates.

Communication: A simple method for simulation of freezing transitions

Despite recent advances, precise simulation of freezing transitions continues to be a challenging task. In this work, a simulation method for fluid-solid transitions is developed. The method is based on a modification of the constrained cell model which was proposed by Hoover and Ree [J. Chem. Phys. 47, 4873 (1967)]. In the constrained cell model, each particle is confined in a single Wigner-Seitz cell. Hoover and Ree pointed out that the fluid and solid phases can be linked together by adding an external field of variable strength. High values of the external field favor single occupancy configurations and thus stabilize the solid phase. In the present work, the modified cell model is simulated in the constant-pressure ensemble using tempering and histogram reweighting techniques. Simulation results on a system of hard spheres indicate that as the strength of the external field is reduced, the transition from solid to fluid is continuous at low and intermediate pressures and discontinuous at high pressures. Fluid-solid coexistence for the hard-sphere model is established by analyzing the phase transition of the modified model in the limit in which the external field vanishes. The coexistence pressure and densities are in excellent agreement with current state-of-the-art techniques.

Precise simulation of the freezing transition of supercritical Lennard-Jones

The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.

Simulation of phase boundaries using constrained cell models

Despite impressive advances, precise simulation of fluid-fluid and fluid-solid phase transitions still remains a challenging task. The present work focuses on the determination of the phase diagram of a system of particles that interact through a pair potential, φ(r), which is of the form φ(r) = 4ε[(σ/r)(2n) - (σ/r)(n)] with n = 12. The vapor-liquid phase diagram of this model is established from constant-pressure simulations and flat-histogram techniques. The properties of the solid phase are obtained from constant-pressure simulations using constrained cell models. In the constrained cell model, the simulation volume is divided into Wigner-Seitz cells and each particle is confined to moving in a single cell. The constrained cell model is a limiting case of a more general cell model which is constructed by adding a homogeneous external field that controls the relative stability of the fluid and the solid phase. Fluid-solid coexistence at a reduced temperature of 2 is established from constant-pressure simulations of the generalized cell model. The previous fluid-solid coexistence point is used as a reference point in the determination of the fluid-solid phase boundary through a thermodynamic integration type of technique based on histogram reweighting. Since the attractive interaction is of short range, the vapor-liquid transition is metastable against crystallization. In the present work, the phase diagram of the corresponding constrained cell model is also determined. The latter is found to contain a stable vapor-liquid critical point and a triple point.

Precise simulation of subcritical freezing using constrained cell models

In simulations of freezing transitions using constrained cell models, the space is divided into Wigner–Seitz cells appropriate for the solid phase under consideration and each particle is confined to move in its own Wigner–Seitz cell. The constrained cell model is a limiting case of a generalized or modified cell model which is constructed by adding a homogeneous external field that controls the relative stability of the two phases. High values of the external field variable force configurations with one particle per Wigner–Seitz cell and thus favor the solid phase. Normal (i.e. unconstrained) behavior is recovered in the limit of vanishing field. In previous work, it was shown that the modified cell model can be used to link the fluid with the solid phase on a constant-pressure (or density) path by progressively increasing the strength of the field. It was found that the passage from the fluid to the solid is continuous at low and moderate pressures. In contrast, at high pressures, the passage from the fluid to the solid occurs via a discontinuous, first-order transition. The special point that separates continuous from discontinuous behaviors is very close to the mechanical stability point of the solid phase. In previous work, the fluid–solid transition of model systems on supercritical isotherms was determined either by analyzing the field-induced transition of the appropriate modified cell model in the zero-field limit or via thermodynamic integration using the same model. In the present work, the fluid–solid transition of the Lennard-Jones model is analyzed on the isotherm that corresponds to a reduced temperature of unity. At this temperature, the pressure-density isotherm of the fluid phase contains a first-order gas–liquid phase transition. Constant-pressure simulations of the constrained cell model indicate that the pressure-density isotherm of the solid phase contains a similar phase transition between a dilute, gas-like and a dense, liquid-like phase, respectively. The ‘gas–liquid’ phase transition of the constrained cell model terminates at a critical point. The fluid–solid transition of the Lennard-Jones model at a reduced temperature of unity is obtained from constant-pressure simulations of the appropriate modified cell model. The size-dependent coexistence pressure and densities are analyzed according to finite-size scaling techniques. As was also emphasized in previous work, the results clearly demonstrate the importance of accounting for size effects in simulations of fluid–solid transitions.

Communication: Direct determination of triple-point coexistence through cell model simulation

In simulations of fluid-solid coexistence, the solid phase is modeled as a constrained system of Wigner-Seitz cells with one particle per cell. This model, commonly referred to as the constrained cell model, is a limiting case of a more general cell model, which is formed by considering a homogeneous external field that controls the number of particles per cell and, hence, the relative stability of the solid against the fluid phase. The generalized cell model provides a link that connects the disordered, fluid phase with the ordered, solid phase. In the present work, the phase diagram of this model is investigated through multicanonical simulations at constant pressure and histogram reweighting techniques for a system of 256 Lennard-Jones particles. The simulation data are used to obtain an estimate of the triple point of the Lennard-Jones system. The triple-point pressure is found to be higher compared to previous work. The likely explanation for this discrepancy is the highly compressible nature of the gas phase.

Communication: Phase transitions, criticality, and three-phase coexistence in constrained cell models

In simulation studies of fluid-solid transitions, the solid phase is usually modeled as a constrained system in which each particle is confined to move in a single Wigner-Seitz cell. The constrained cell model has been used in the determination of fluid-solid coexistence via thermodynamic integration and other techniques. In the present work, the phase diagram of such a constrained system of Lennard-Jones particles is determined from constant-pressure simulations. The pressure-density isotherms exhibit inflection points which are interpreted as the mechanical stability limit of the solid phase. The phase diagram of the constrained system contains a critical and a triple point. The temperature and pressure at the critical and the triple point are both higher than those of the unconstrained system due to the reduction in the entropy caused by the single occupancy constraint.

Modeling and control of protein crystal shape distribution

The production of highly ordered, high quality protein crystals through batch crystallization processes is vital in devising proteins for therapeutic purposes in a number of diseases. Additionally, protein crystallization is a central activity in the pharmaceutical industry. The present work focuses on the modeling and control for a population of tetragonal hen egg-white (HEW) lysozyme protein crystals. First, a model is presented which will consider nucleation of lysozyme crystals followed by kinetic Monte Carlo (kMC) simulations to model the crystal growth on the (110) and (101) faces, respectively. These kMC simulations comprise of adsorption, desorption, and migration events where the rate equations for each type of event are similar to those of Durbin and Feher [10]. The computation of the growth rate for each face requires the use of kMC simulations due to the dependence of the desorption and migration rates on the surface micro-configuration, and thus it cannot be computed simply by subtracting the adsorption and desorption rates. Next, the data obtained from the kMC simulations will be used to generate a nonlinear algebraic equation which relates the solute concentration and temperature to the growth rate ratio between the two independent crystal faces. A model predictive controller will use this nonlinear equation to regulate the protein crystals to desired shapes in the presence of disturbance in the operating conditions. The proposed method demonstrates that it can successfully achieve the desired crystal shapes which range from equidimensional to more elongated type of structures for the entire crystal population while in the presence of arbitrary variations in the solute concentration.