Dynamical Approach to the Jamming Problem.

A simple dynamical model, biased random organization (BRO), appears to produce configurations known as random close packing (RCP) as BRO's densest critical point in dimension d=3. We conjecture that BRO likewise produces RCP in any dimension; if so, then RCP does not exist in d=1-2 (where BRO dynamics lead to crystalline order). In d=3-5, BRO produces isostatic configurations and previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively. For all investigated dimensions (d=2-5), we find that BRO belongs to the Manna universality class of dynamical phase transitions by measuring critical exponents associated with the steady-state activity and the long-range density fluctuations. Additionally, BRO's distribution of near contacts (gaps) displays behavior consistent with the infinite-dimensional theoretical treatment of RCP when d≥4. The association of BRO's densest critical configurations with random close packing implies that RCP's upper-critical dimension is consistent with the Manna class d_{uc}=4.

Harnessing Peptide Binding to Capture and Reclaim Phosphate.

With rising consumer demands, society is tapping into wastewater as an innovative source to recycle depleting resources. Novel reclamation technologies have been recently explored for this purpose, including several that optimize natural biological processes for targeted reclamation. However, this emerging field has a noticeable dearth of synthetic material technologies that are programmed to capture, release, and recycle specified targets; and of the novel materials that do exist, synthetic platforms incorporating biologically inspired mechanisms are rare. We present here a prototype of a materials platform utilizing peptide amphiphiles that has been molecularly engineered to sequester, release, and reclaim phosphate through a stimuli-responsive pH trigger, exploiting a protein-inspired binding mechanism that is incorporated directly into the self-assembled material network. This material is able to harvest and controllably release phosphate for multiple cycles of reuse, and it is selective over nitrate and nitrite. We have determined by simulations that the binding conformation of the peptide becomes constrained in the dense micelle corona at high pH such that phosphate is expelled when it otherwise would be preferentially bound. However, at neutral pH, this dense structure conversely employs multichain binding to further stabilize phosphate when it would otherwise be unbound, opening opportunities for higher-order conformational binding design to be engineered into this controllably packed corona. With this work, we are pioneering a new platform to be readily altered to capture other valuable targets, presenting a new class of capture and release materials for recycling resources on the nanoscale.

Combined Force-Frequency Sampling for Simulation of Systems Having Rugged Free Energy Landscapes.

An adaptive, machine learning-based sampling method is presented for simulation of systems having rugged, multidimensional free energy landscapes. The method's main strength resides in its ability to learn both from the frequency of visits to distinct states and the generalized force estimates that arise in a system as it evolves in phase space. This is accomplished by introducing a self-integrating artificial neural network, which generates an estimate of the free energy directly from its derivatives. The usefulness of the proposed combined approach is examined in the context of two concrete examples, namely, an alanine dipeptide molecule in water and a polymer diffusing through a narrow pore. This new method is found to be robust, faster, and more accurate than approaches that rely only on frequency-based or generalized force-based estimations. After combining the proposed approach with overfill protection and support for sparse data storage and training, the method is shown to be more effective than comparable, previously available techniques and capable of scaling efficiently to larger numbers of collective variables.

Free energy of metal-organic framework self-assembly.

Metal-organic frameworks (MOFs) represent an important class of materials. Careful selection of building blocks allows for tailoring of the properties of the resulting framework. The self-assembly process, however, is not understood, and without detailed knowledge of the underlying molecular mechanism, it is difficult to anticipate whether a particular design can be realized, or whether the material adopts a metastable, kinetically arrested state. We present a detailed examination of early-stage self-assembly pathways of the MOF-5. Enhanced sampling techniques are used to model a self-assembly in an explicit solvent (dimethylformamide, DMF). We identify several free energy barriers encountered during the assembly of the final MOF, which arise from structural rearrangements preceding MOF formation and from disrupted MOF-solvent interactions as formation proceeds. In all cases considered here, MOFs exhibit favorable entropic gains during the assembly. More generally, the strategy presented provides a step toward the experimental design characterizing the formation of ordered frameworks and possible sources of polymorphism.

Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning.

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.

Early-stage human islet amyloid polypeptide aggregation: Mechanisms behind dimer formation.

Amyloid aggregates of human islet amyloid polypeptide (hIAPP or human amylin) have long been implicated in the development of type II diabetes. While hIAPP is known to aggregate into amyloid fibrils, it is the early-stage prefibrillar species that have been proposed to be cytotoxic. A detailed picture of the early-stage aggregation process and relevant intermediates would be valuable in the development of effective therapeutics. Here, we use atomistic molecular dynamics simulations with a combination of enhanced sampling methods to examine the formation of the hIAPP dimer in water. Bias-exchange metadynamics calculations reveal relative conformational stabilities of the hIAPP dimer. Finite temperature string method calculations identify pathways for dimer formation, along with relevant free energy barriers and intermediate structures. We show that the initial stages of dimerization involve crossing a substantial free energy barrier to form an intermediate structure exhibiting transient ß-sheet character, before proceeding to form an entropically stabilized dimer structure.

Adaptive enhanced sampling by force-biasing using neural networks.

A machine learning assisted method is presented for molecular simulation of systems with rugged free energy landscapes. The method is general and can be combined with other advanced sampling techniques. In the particular implementation proposed here, it is illustrated in the context of an adaptive biasing force approach where, rather than relying on discrete force estimates, one can resort to a self-regularizing artificial neural network to generate continuous, estimated generalized forces. By doing so, the proposed approach addresses several shortcomings common to adaptive biasing force and other algorithms. Specifically, the neural network enables (1) smooth estimates of generalized forces in sparsely sampled regions, (2) force estimates in previously unexplored regions, and (3) continuous force estimates with which to bias the simulation, as opposed to biases generated at specific points of a discrete grid. The usefulness of the method is illustrated with three different examples, chosen to highlight the wide range of applicability of the underlying concepts. In all three cases, the new method is found to enhance considerably the underlying traditional adaptive biasing force approach. The method is also found to provide improvements over previous implementations of neural network assisted algorithms.

SSAGES: Software Suite for Advanced General Ensemble Simulations.

Molecular simulation has emerged as an essential tool for modern-day research, but obtaining proper results and making reliable conclusions from simulations requires adequate sampling of the system under consideration. To this end, a variety of methods exist in the literature that can enhance sampling considerably, and increasingly sophisticated, effective algorithms continue to be developed at a rapid pace. Implementation of these techniques, however, can be challenging for experts and non-experts alike. There is a clear need for software that provides rapid, reliable, and easy access to a wide range of advanced sampling methods and that facilitates implementation of new techniques as they emerge. Here we present SSAGES, a publicly available Software Suite for Advanced General Ensemble Simulations designed to interface with multiple widely used molecular dynamics simulations packages. SSAGES allows facile application of a variety of enhanced sampling techniques-including adaptive biasing force, string methods, and forward flux sampling-that extract meaningful free energy and transition path data from all-atom and coarse-grained simulations. A noteworthy feature of SSAGES is a user-friendly framework that facilitates further development and implementation of new methods and collective variables. In this work, the use of SSAGES is illustrated in the context of simple representative applications involving distinct methods and different collective variables that are available in the current release of the suite. The code may be found at: https://github.com/MICCoM/SSAGES-public.