Sterically Driven Current Reversal in a Model Molecular Motor

Simulations can help unravel the complicated ways in which molecular structure determines function. Here, we use molecular simulations to show how slight alterations of a molecular motor's structure can cause the motor's typical dynamical behavior to reverse directions. Inspired by autonomous synthetic catenane motors, we study the molecular dynamics of a minimal motor model, consisting of a shuttling ring that moves along a track containing interspersed binding sites and catalytic sites. The binding sites attract the shuttling ring while the catalytic sites speed up a reaction between molecular species, which can be thought of as fuel and waste. When that fuel and waste are held in a nonequilibrium steady-state concentration, the free energy from the reaction drives directed motion of the shuttling ring along the track. Using this model and nonequilibrium molecular dynamics, we show that the shuttling ring's direction can be reversed by simply adjusting the spacing between binding and catalytic sites on the track. We present a steric mechanism behind the current reversal, supported by kinetic measurements from the simulations. These results demonstrate how molecular simulation can guide future development of artificial molecular motors

Effects of excluded volume and hydrodynamic interactions on the behavior of isolated bead‐rod polymer chains in shearing flow

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106769/1/aic14317.pd

Simulating a Chemically-Fueled Molecular Motor with Nonequilibrium Molecular Dynamics

Most computer simulations of molecular dynamics take place under equilibrium conditions--in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequilibrium steady state. We develop such a dynamic scheme and use it to observe cycles of a new particle-based classical model of a catenane-like molecular motor. Molecular motors are frequently modeled with detailed-balance-breaking Markov models, and we explicitly construct such a picture by coarse graining the microscopic dynamics of our simulations in order to extract rates. This work identifies inter-particle interactions that tune those rates to create a functional motor, thereby yielding a computational playground to investigate the interplay between directional bias, current generation, and coupling strength in molecular information ratchets.Comment: 11 pages, 7 figures plus Supporting Informatio

Improved Methods for Polarizable Classical Molecular Dynamics Simulations

Polarization is the ability of a molecule’s electron density to respond to and influence its environment and is the leading order many-body interaction for advanced electrostatics used in classical molecular simulation. It has proven to be an important interaction that is necessary to accurately simulate certain molecular systems. Polarization helps to capture intermolecular interactions of ligand-macromolecule complexes, heterogeneity at interfaces, electric field environments of heterogeneous systems such as proteins, and structure and dynamics of peptide-water solutions. In general, systems that can benefit most from the inclusion of polarization effects are heterogeneous, non-bulk systems that give rise to asymmetric environments. Additionally, polarization has been shown to be more transferable across the phase diagram beyond regions where the force field was initially parameterized.The main drawback of including polarization in molecular simulation, however, is the computational expense of calculating explicit polarization interactions. The most common approach is to approximate the polarization solution using an iterative self- consistent field (SCF) method, which accounts for about half the cost of a polarizable simulation. Another approach is that of extended Lagrangians (EL), which treat polarization degrees of freedom dynamically and do not require iterations. EL methods, however, suffer from instability and require prohibitively small simulation time steps.The focus of this dissertation is the reduction of the computational cost of polarizable classical molecular simulations while maintaining the high level of accuracy associated with these simulations. I present several new methods that combine the stability of SCF methods with the iteration-free dynamics of EL methods into a hybrid EL/SCF framework. The key to these EL/SCF methods is the introduction of auxiliary polarization degrees of freedom, which can be dynamically integrated and drive the real polarization degrees of freedom. The first approach is a relatively simple method for polarization that reduces the number of iterative cycles required for an SCF solution. This method also introduces thermostat control of auxiliary variables and is called iEL/SCF. A more sophisticated approach that eliminates the need for SCF iteration altogether, iEL/0-SCF, is also presented. This method is developed for both induced dipole and Drude polarization models. I also present a generalized and complete theory for classical iteration-free polarizable EL/SCF dynamics and explore combining iteration- free dynamics with other advanced high efficiency methods such as RESPA multi-time stepping and stochastic-isokinetic integration, which work complementarily with EL/SCF to further increase computational efficiency.In summary, the developments presented in this dissertation are methods and theories that significantly reduce the cost of classical polarizable molecular dynamics without sacrificing accuracy. This work represents an important step in moving the scientific community toward the broader adoption of advanced potential energy surfaces embodied by polarizable force fields

An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction.

We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the course of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well

A New Method for Treating Drude Polarization in Classical Molecular Simulation

With polarization becoming an increasingly common feature in classical molecular simulation, it is important to develop methods that can efficiently and accurately evaluate the many-body polarization solution. In this work, we expand the theoretical framework of our inertial extended Langrangian, self-consistent field iteration-free method (iEL/0-SCF), introduced for point induced dipoles, to the polarization model of a Drude oscillator. When applied to the polarizable simple point charge model (PSPC) for water, our iEL/0-SCF method for Drude polarization is as stable as a well-converged SCF solution and more stable than traditional extended Lagrangian (EL) approaches or EL formulations based on two temperature ensembles where Drude particles are kept “colder” than the real degrees of freedom. We show that the iEL/0-SCF method eliminates the need for mass repartitioning from parent atoms onto Drude particles, obeys system conservation of linear and angular momentum, and permits the extension of the integration time step of a basic molecular dynamics simulation to 6.0 fs for PSPC water

Accurate Classical Polarization Solution with No Self-Consistent Field Iterations.

We present a new solution for classical polarization that does not require any self-consistent field iterations, the aspect of classical polarization that makes it computationally expensive. The new method builds upon our iEL/SCF Lagrangian scheme that defines a set of auxiliary induced dipoles whose original purpose was to serve as a time-reversible initial guess to the SCF solution of the set of real induced dipoles. In the new iEL/0-SCF approach the auxiliary dipoles now drive the time evolution of the real induced dipoles such that they stay close to the Born-Oppenheimer surface in order to achieve a truly SCF-less method. We show that the iEL/0-SCF exhibits no loss of simulation accuracy when analyzed across bulk water, low to high concentration salt solutions, and small solutes to large proteins in water. In addition, iEL/0-SCF offers significant computational savings over more expensive SCF calculations based on traditional 1 fs time step integration using symplectic integrators and is as fast as reversible reference system propagator algorithms with an outer 2 fs time step