Mechanically driven unfolding is a useful computational tool for extracting the energetics and stretching pathway of peptides. In this work, two representative β-hairpin peptides, chignolin (PDB: 1UAO) and trpzip1 (PDB: 1LE0), were investigated using an adaptive variant of the original steered molecular dynamics method called adaptive steered molecular dynamics (ASMD). The ASMD method makes it possible to perform energetic calculations on increasingly complex biological systems. Although the two peptides are similar in length and have similar secondary structures, their unfolding energetics are quite different. The hydrogen bonding profile and specific residue pair interaction energies provide insight into the differing stabilities of these peptides and reveal which of the pairs provides the most significant stabilization.

The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter–Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.

Transition-state theories describing barrierless chemical reactions, or more general activated problems, are often hampered by the lack of a saddle around which the dividing surface can be constructed. For example, the time-dependent transition-state trajectory uncovering the nonrecrossing dividing surface in thermal reactions in the framework of the Langevin equation has relied on perturbative approaches in the vicinity of the saddle. We recently obtained an alternative approach using Lagrangian descriptors to construct time-dependent and recrossing-free dividing surfaces. This is a nonperturbative approach making no reference to a putative saddle. Here we show how the Lagrangian descriptor can be used to obtain the transition-state geometry of a dissipated and thermalized reaction across barrierless potentials. We illustrate the method in the case of a 1D Brownian motion for both barrierless and step potentials; however, the method is not restricted and can be directly applied to different kinds of potentials and higher dimensional systems.

The surface coverage of coarse-grained macromolecules bound to a solid substrate is not simply proportional to the two-dimensional number density because macromolecules can overlap. As a function of the overlap probability δ, we have developed analytical formulas and computational models capable of characterizing this nonlinear relationship. For simplicity, we ignore site–site interactions that would be induced by length-scale mismatches between binding sites and the radius of gyration of the incident coarse-grained macromolecular species. The interactions between macromolecules are modeled with a finite bounded potential that allows multiple macromolecules to occupy the same binding site. The softness of the bounded potential is thereby reduced to the single parameter δ. Through variation of this parameter, completely hard (δ = 0) and completely soft (δ = 1) behavior can be bridged. For soft macromolecular interactions (δ > 0), multiple occupancy reduces the fraction of sites ϕ occupied on the substrate. We derive the exact transition probability between sequential configurations and use this probability to predict ϕ and the distribution of occupied sites. Due to the complexity of the exact ϕ expressions and their analytical intractability at the thermodynamic limit, we apply a simplified mean-field (MF) expression for ϕ. The MF model is found to be in excellent agreement with the exact result. Both the exact and MF models are applied to an example dynamical system with multibody interactions governed by a stochastic bounded potential. Both models show agreement with results measured from simulation.

Diffusional behavior of a spherical probe through static nematogens (or needles) is probed via molecular dynamics simulations. The needles are modeled as spherocylinders and are arranged in idealized limits of an isotropic phase and a slowly quenched nematic mesh. The spherical probe exhibits superdiffusive motion through both the isotropic and nematic scatterer configurations. The superdiffusive behavior results from directional collisions between the spherical probe and the static nematogens. Velocity autocorrelation functions show long time correlations caused by directionality of transport due to the geometric anisotropy of the scatterers; however, glassy behavior exhibited by the tracer is observed when the scatterers are sufficiently long, leading to a downturn in the diffusion coefficients. Diffusion through the nematic configuration shows anisotropic diffusion with preferential motion occurring along the orientational director by way of effective channels formed by the long-range orientational order of the aligned nematogens.

The existence of three regimes in the dynamics of a thin needle-like particle diffusing through a two-dimensional random array of scatterers as the needle length is varied relative to the scatterer density was previously seen in a series of simulations. The first regime occurs at low density when the needle’s diffusion follows the expected Enskog behavior. An intermediate regime gives rise to enhanced diffusion after a critical density of scatterers is reached, a manifestation of the suppression of librational motion as the needle is confined to effectively thinner but longer tubes. The third regime occurs at high scatterer density with the particle dynamics characteristic of a glass. In this article, we investigate whether the tubes seen in the second regime persist in a three-dimensional array of scatterers. The fact that the enhanced regime is not observed in a three-dimensional random array of scatterers suggests that the effective tubes formed by the moving needle are fragile structures highly dependent on dimensionality.

The long-time correlation functions of an infinitesimally thin needle moving through stationary point scatterers—a so-called Lorentz model—exhibits surprisingly long-time tails. These long-time tails are now seen to persist in a two-dimensional model even when the needle has a finite thickness. If the needles are too thick, then the needles are effectively trapped at all nontrivial densities of the scatterers. At needle widths approximately equal to or smaller than σ = ε/20 where ε is the average spacing between scatterers, the needle diffuses and exhibits the crossover transition from the expected Enskog behavior to the enhanced translation diffusion seen earlier by Höfling, Frey and Franosch [ Phys. Rev. Lett. 2008, 101, 120605]. At this needle width, an increase in its center-of-mass diffusion with respect to increasing density is seen after a crossover density of n* ≈ 5 is reached. (The reduced density n* is defined as n* = nL2 where n is the number density of particles and L is the needle length.) The crossover transition for needles with finite thickness is spread over a range of densities exhibiting intermediate behavior. The asymptotic divergence of the center of mass diffusion is suppressed compared to that of infinitely thin needles. Finally, a new diminished diffusion regime, apparently due to the increased importance of head-on collisions, now appears at high scattering densities.

The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory—that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.

The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter–Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.

Reaction rates across time-dependent barriers are difficult to define and difficult to obtain using standard transition state theory approaches because of the complexity of the geometry of the dividing surface separating reactants and products. Using perturbation theory (PT) or Lagrangian descriptors (LDs), we can obtain the transition state trajectory and the associated recrossing-free dividing surface. With the latter, we are able to determine the exact reactant population decay and the corresponding rates to benchmark the PT and LD approaches. Specifically, accurate rates are obtained from a local description regarding only direct barrier crossings and to those obtained from a stability analysis of the transition state trajectory. We find that these benchmarks agree with the PT and LD approaches for obtaining recrossing-free dividing surfaces. This result holds not only for the local dynamics in the vicinity of the barrier top, but also for the global dynamics of particles that are quenched at the reactant or product wells after their sojourn over the barrier region. The double-well structure of the potential allows for long-time dynamics related to collisions with the outside walls that lead to long-time returns in the low-friction regime. This additional global dynamics introduces slow-decay pathways that do not result from the local transition across the recrossing-free dividing surface associated with the transition state trajectory, but can be addressed if that structure is augmented by the population transfer of the long-time returns.