Remembering the Work of Phillip L. Geissler: A Coda to His Scientific Trajectory.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers.

Erratum: Cooperative Gas Adsorption without a Phase Transition in Metal-Organic Frameworks [Phys. Rev. Lett. 121, 015701 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.015701.

Dynamics of Polymer Nanocapsule Buckling and Collapse Revealed by In Situ Liquid-Phase TEM.

Nanocapsules are hollow nanoscale shells that have applications in drug delivery, batteries, self-healing materials, and as model systems for naturally occurring shell geometries. In many applications, nanocapsules are designed to release their cargo as they buckle and collapse, but the details of this transient buckling process have not been directly observed. Here, we use in situ liquid-phase transmission electron microscopy to record the electron-irradiation-induced buckling in spherical 60-187 nm polymer capsules with ∼3.5 nm walls. We observe in real time the release of aqueous cargo from these nanocapsules and their buckling into morphologies with single or multiple indentations. The in situ buckling of nanoscale capsules is compared to ex situ measurements of collapsed and micrometer-sized capsules and to Monte Carlo (MC) simulations. The shape and dynamics of the collapsing nanocapsules are consistent with MC simulations, which reveal that the excessive wrinkling of nanocapsules with ultrathin walls results from their large Föppl-von Kármán numbers around 105. Our experiments suggest design rules for nanocapsules with the desired buckling response based on parameters such as capsule radius, wall thickness, and collapse rate.

Low-dissipation self-assembly protocols of active sticky particles.

We use neuroevolutionary learning to identify time-dependent protocols for low-dissipation self-assembly in a model of generic active particles with interactions. When the time allotted for assembly is sufficiently long, low-dissipation protocols use only interparticle attractions, producing an amount of entropy that scales as the number of particles. When time is too short to allow assembly to proceed via diffusive motion, low-dissipation assembly protocols instead require particle self-propulsion, producing an amount of entropy that scales with the number of particles and the swim length required to cause assembly. Self-propulsion therefore provides an expensive but necessary mechanism for inducing assembly when time is of the essence.

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly.

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. The learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

Dynamical Large Deviations of Two-Dimensional Kinetically Constrained Models Using a Neural-Network State Ansatz.

We use a neural-network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We use recurrent neural networks to describe the large deviations of the dynamical activity of model glasses, kinetically constrained models in two dimensions. We present the first finite size-scaling analysis of the large-deviation functions of the two-dimensional Fredrickson-Andersen model, and explore the spatial structure of the high-activity sector of the South-or-East model. These results provide a new route to the study of dynamical large-deviation functions, and highlight the broad applicability of the neural-network state ansatz across domains in physics.

Decorated networks of native proteins: nanomaterials with tunable mesoscopic domain size.

Natural and artificial proteins with designer properties and functionalities offer unparalleled opportunity for functional nanoarchitectures formed through self-assembly. However, to exploit this potential we need to design the system such that assembly results in desired architecture forms while avoiding denaturation and therefore retaining protein functionality. Here we address this challenge with a model system of fluorescent proteins. By manipulating self-assembly using techniques inspired by soft matter where interactions between the components are controlled to yield the desired structure, we have developed a methodology to assemble networks of proteins of one species which we can decorate with another, whose coverage we can tune. Consequently, the interfaces between domains of each component can also be tuned, with potential applications for example in energy - or electron - transfer. Our model system of eGFP and mCherry with tuneable interactions reveals control over domain sizes in the resulting networks.

Peptoid nanosheets exhibit a new secondary-structure motif.

A promising route to the synthesis of protein-mimetic materials that are capable of complex functions, such as molecular recognition and catalysis, is provided by sequence-defined peptoid polymers--structural relatives of biologically occurring polypeptides. Peptoids, which are relatively non-toxic and resistant to degradation, can fold into defined structures through a combination of sequence-dependent interactions. However, the range of possible structures that are accessible to peptoids and other biological mimetics is unknown, and our ability to design protein-like architectures from these polymer classes is limited. Here we use molecular-dynamics simulations, together with scattering and microscopy data, to determine the atomic-resolution structure of the recently discovered peptoid nanosheet, an ordered supramolecular assembly that extends macroscopically in only two dimensions. Our simulations show that nanosheets are structurally and dynamically heterogeneous, can be formed only from peptoids of certain lengths, and are potentially porous to water and ions. Moreover, their formation is enabled by the peptoids' adoption of a secondary structure that is not seen in the natural world. This structure, a zigzag pattern that we call a Σ('sigma')-strand, results from the ability of adjacent backbone monomers to adopt opposed rotational states, thereby allowing the backbone to remain linear and untwisted. Linear backbones tiled in a brick-like way form an extended two-dimensional nanostructure, the Σ-sheet. The binary rotational-state motif of the Σ-strand is not seen in regular protein structures, which are usually built from one type of rotational state. We also show that the concept of building regular structures from multiple rotational states can be generalized beyond the peptoid nanosheet system.

Deposition control of model glasses with surface-mediated orientational order.

We introduce a minimal model of solid-forming anisotropic molecules that displays, in thermal equilibrium, surface orientational order without bulk orientational order. The model reproduces the nonequilibrium behavior of recent experiments in which a bulk nonequilibrium structure grown by deposition contains regions of orientational order characteristic of the surface equilibrium. This order is deposited, in general, in a nonuniform way because of the emergence of a growth-poisoning mechanism that causes equilibrated surfaces to grow slower than non-equilibrated surfaces. We use evolutionary methods to design oscillatory protocols able to grow nonequilibrium structures with uniform order, demonstrating the potential of protocol design for the fabrication of this class of materials.

Hysteresis curves reveal the microscopic origin of cooperative CO2 adsorption in diamine-appended metal-organic frameworks.

Diamine-appended metal-organic frameworks (MOFs) of the form Mg2(dobpdc)(diamine)2 adsorb CO2 in a cooperative fashion, exhibiting an abrupt change in CO2 occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a first-order phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO2 chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, providing a physical understanding of cooperative adsorption in this industrially important class of materials.

Conformations of peptoids in nanosheets result from the interplay of backbone energetics and intermolecular interactions.

The conformations adopted by the molecular constituents of a supramolecular assembly influence its large-scale order. At the same time, the interactions made in assemblies by molecules can influence their conformations. Here we study this interplay in extended flat nanosheets made from nonnatural sequence-specific peptoid polymers. Nanosheets exist because individual polymers can be linear and untwisted, by virtue of polymer backbone elements adopting alternating rotational states whose twists oppose and cancel. Using molecular dynamics and quantum mechanical simulations, together with experimental data, we explore the design space of flat nanostructures built from peptoids. We show that several sets of peptoid backbone conformations are consistent with their being linear, but the specific combination observed in experiment is determined by a combination of backbone energetics and the interactions made within the nanosheet. Our results provide a molecular model of the peptoid nanosheet consistent with all available experimental data and show that its structure results from a combination of intra- and intermolecular interactions.

Improving the Accuracy of Nearest-Neighbor Classification Using Principled Construction and Stochastic Sampling of Training-Set Centroids.

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using coarse-graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that a principled coarse-graining algorithm can convert training images into fewer image centroids without loss of accuracy of classification of test-set images by nearest-neighbor classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. On the MNIST and Fashion-MNIST data sets this approach converts nearest-neighbor classification from a mid-ranking- to an upper-ranking member of the set of classical machine-learning techniques.

Evolutionary reinforcement learning of dynamical large deviations.

We show how to bound and calculate the likelihood of dynamical large deviations using evolutionary reinforcement learning. An agent, a stochastic model, propagates a continuous-time Monte Carlo trajectory and receives a reward conditioned upon the values of certain path-extensive quantities. Evolution produces progressively fitter agents, potentially allowing the calculation of a piece of a large-deviation rate function for a particular model and path-extensive quantity. For models with small state spaces, the evolutionary process acts directly on rates, and for models with large state spaces, the process acts on the weights of a neural network that parameterizes the model's rates. This approach shows how path-extensive physics problems can be considered within a framework widely used in machine learning.

Insights into the Structure and Energy of DNA Nanoassemblies.

Since the pioneering work of Ned Seeman in the early 1980s, the use of the DNA molecule as a construction material experienced a rapid growth and led to the establishment of a new field of science, nowadays called structural DNA nanotechnology. Here, the self-recognition properties of DNA are employed to build micrometer-large molecular objects with nanometer-sized features, thus bridging the nano- to the microscopic world in a programmable fashion. Distinct design strategies and experimental procedures have been developed over the years, enabling the realization of extremely sophisticated structures with a level of control that approaches that of natural macromolecular assemblies. Nevertheless, our understanding of the building process, i.e., what defines the route that goes from the initial mixture of DNA strands to the final intertwined superstructure, is, in some cases, still limited. In this review, we describe the main structural and energetic features of DNA nanoconstructs, from the simple Holliday junction to more complicated DNA architectures, and present the theoretical frameworks that have been formulated until now to explain their self-assembly. Deeper insights into the underlying principles of DNA self-assembly may certainly help us to overcome current experimental challenges and foster the development of original strategies inspired to dissipative and evolutive assembly processes occurring in nature.

Stereochemistry of polypeptoid chain configurations.

Like polypeptides, peptoids, or N-substituted glycine oligomers, have intrinsic conformational preferences due to their amide backbones and close spacing of side chain substituents. However, the conformations that peptoids adopt are distinct from polypeptides due to several structural differences: the peptoid backbone is composed of tertiary amide bonds that have trans and cis conformers similar in energy, they lack a backbone hydrogen bond donor, and have an N-substituent. To better understand how these differences manifest in actual peptoid structures, we analyzed 46 high quality, experimentally determined peptoid structures reported in the literature to extract their backbone conformational preferences. One hundred thirty-two monomer dihedral angle pairs were compared to the calculated energy landscape for the peptoid Ramachandran plot, and were found to fall within the expected minima. Interestingly, only two regions of the backbone dihedral angles ϕ and ψ were found to be populated that are mirror images of each other. Furthermore, these two conformers are present in both cis and trans forms. Thus, there are four primary conformers that are sufficient to describe almost all known backbone conformations for peptoid oligomers, despite conformational constraints imposed by a variety of side chains, macrocyclization, or crystal packing forces. Because these conformers are predominant in peptoid structure, and are distinct from those found in protein secondary structures, we propose a simple naming system to aid in the description and classification of peptoid structure.

Unconstrained peptoid tetramer exhibits a predominant conformation in aqueous solution.

Conformational control in peptoids, N-substituted glycines, is crucial for the design and synthesis of biologically-active compounds and atomically-defined nanomaterials. While there are a growing number of structural studies in solution, most have been performed with conformationally-constrained short sequences (e.g., sterically-hindered sidechains or macrocyclization). Thus, the inherent degree of heterogeneity of unconstrained peptoids in solution remains largely unstudied. Here, we explored the folding landscape of a series of simple peptoid tetramers in aqueous solution by NMR spectroscopy. By incorporating specific 13 C-probes into the backbone using bromoacetic acid-2-13 C as a submonomer, we developed a new technique for sequential backbone assignment of peptoids based on the 1,n-Adequate pulse sequence. Unexpectedly, two of the tetramers, containing an N-(2-aminoethyl)glycine residue (Nae), had preferred conformations. NMR and molecular dynamics studies on one of the tetramers showed that the preferred conformer (52%) had a trans-cis-trans configuration about the three amide bonds. Moreover, >80% of the ensemble contained a cis amide bond at the central amide. The backbone dihedral angles observed fall directly within the expected minima in the peptoid Ramachandran plot. Analysis of this compound against similar peptoid analogs suggests that the commonly used Nae monomer plays a key role in the stabilization of peptoid structure via a side-chain-to-main-chain interaction. This discovery may offer a simple, synthetically high-yielding approach to control peptoid structure, and suggests that peptoids have strong intrinsic conformational preferences in solution. These findings should facilitate the predictive design of folded peptoid structures, and accelerate application in areas ranging from drug discovery to biomimetic nanoscience.

Cooperative Gas Adsorption without a Phase Transition in Metal-Organic Frameworks.

Cooperative adsorption of gases by porous frameworks, which permits more efficient uptake and removal than the more usual noncooperative (Langmuir-type) adsorption, usually results from a phase transition of the framework. Here we show how cooperativity emerges in the class of metal-organic frameworks mmen-M_{2}(dobpdc) in the absence of a phase transition. Our study provides a microscopic understanding of the emergent features of cooperative binding, including the position, slope, and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.

Strong bonds and far-from-equilibrium conditions minimize errors in lattice-gas growth.

We use computer simulation to study the layer-by-layer growth of particle structures in a lattice gas, taking the number of incorporated vacancies as a measure of the quality of the grown structure. A dynamic scaling relation describes the quality of structures in and out of equilibrium and reveals that the highest-quality structures are obtained, for fixed observation time, using strong interactions and far-from-equilibrium growth conditions. This result contrasts with the usual assumption that weak interactions and mild nonequilibrium conditions are the best way to minimize errors during assembly.

Phase separation and large deviations of lattice active matter.

Off-lattice active Brownian particles form clusters and undergo phase separation even in the absence of attractions or velocity-alignment mechanisms. Arguments that explain this phenomenon appeal only to the ability of particles to move persistently in a direction that fluctuates, but existing lattice models of hard particles that account for this behavior do not exhibit phase separation. Here we present a lattice model of active matter that exhibits motility-induced phase separation in the absence of velocity alignment. Using direct and rare-event sampling of dynamical trajectories, we show that clustering and phase separation are accompanied by pronounced fluctuations of static and dynamic order parameters. This model provides a complement to off-lattice models for the study of motility-induced phase separation.

Heterogeneity of functional groups in a metal-organic framework displays magic number ratios.

Multiple organic functionalities can now be apportioned into nanoscale domains within a metal-coordinated framework, posing the following question: how do we control the resulting combination of "heterogeneity and order"? Here, we report the creation of a metal-organic framework, MOF-2000, whose two component types are incorporated in a 2:1 ratio, even when the ratio of component types in the starting solution is varied by an order of magnitude. Statistical mechanical modeling suggests that this robust 2:1 ratio has a nonequilibrium origin, resulting from kinetic trapping of component types during framework growth. Our simulations show how other "magic number" ratios of components can be obtained by modulating the topology of a framework and the noncovalent interactions between component types, a finding that may aid the rational design of functional multicomponent materials.