Phillip L. Geissler

DRYING-MEDIATED SELF-ASSEMBLY OF NANOPARTICLES

Systems far from equilibrium can exhibit complex transitory structures, even when equilibrium fluctuations are mundane. A dramatic example of this phenomenon has recently been demonstrated for thin-film solutions of passivated nanocrystals during the irreversible evaporation of the solvent. The relatively weak attractions between nanocrystals, which are efficiently screened in solution, become manifest as the solvent evaporates, initiating assembly of intricate, slowly evolving structures. Although certain aspects of this aggregation process can be explained using thermodynamic arguments alone, it is in principle a non-equilibrium process. A representation of this process as arising from the phase separation between a dense nanocrystal ‘liquid’ and dilute nanocrystal ‘vapour’ captures some of the behaviour observed in experiments, but neglects entirely the role of solvent fluctuations, which can be considerable on the nanometre length scale. Here we present a coarse-grained model of nanoparticle self-assembly that explicitly includes the dynamics of the evaporating solvent. Simulations using this model not only account for all observed spatial and temporal patterns, but also predict network structures that have yet to be explored. Two distinct mechanisms of ordering emerge, corresponding to the homogeneous and heterogeneous limits of evaporation dynamics. Our calculations show how different choices of solvent, nanoparticle size (and identity) and thermodynamic state give rise to the various morphologies of the final structures. The resulting guide for designing statistically patterned arrays of nanoparticles suggests the possibility of fabricating spontaneously organized nanoscale devices.

Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices

Understanding how polyhedra pack into extended arrangements is integral to the design and discovery of crystalline materials at all length scales. Much progress has been made in enumerating and characterizing the packing of polyhedral shapes, and the self-assembly of polyhedral nanocrystals into ordered superstructures. However, directing the self-assembly of polyhedral nanocrystals into densest packings requires precise control of particle shape, polydispersity, interactions and driving forces. Here we show with experiment and computer simulation that a range of nanoscale Ag polyhedra can self-assemble into their conjectured densest packings. When passivated with adsorbing polymer, the polyhedra behave as quasi-hard particles and assemble into millimetre-sized three-dimensional supercrystals by sedimentation. We also show, by inducing depletion attraction through excess polymer in solution, that octahedra form an exotic superstructure with complex helical motifs rather than the densest Minkowski lattice. Such large-scale Ag supercrystals may facilitate the design of scalable three-dimensional plasmonic metamaterials for sensing, nanophotonics and photocatalysis.

Membrane bending by protein–protein crowding

Curved membranes are an essential feature of dynamic cellular structures, including endocytic pits, filopodia protrusions and most organelles. It has been proposed that specialized proteins induce curvature by binding to membranes through two primary mechanisms: membrane scaffolding by curved proteins or complexes; and insertion of wedge-like amphipathic helices into the membrane. Recent computational studies have raised questions about the efficiency of the helix-insertion mechanism, predicting that proteins must cover nearly 100% of the membrane surface to generate high curvature, an improbable physiological situation. Thus, at present, we lack a sufficient physical explanation of how protein attachment bends membranes efficiently. On the basis of studies of epsin1 and AP180, proteins involved in clathrin-mediated endocytosis, we propose a third general mechanism for bending fluid cellular membranes: protein–protein crowding. By correlating membrane tubulation with measurements of protein densities on membrane surfaces, we demonstrate that lateral pressure generated by collisions between bound proteins drives bending. Whether proteins attach by inserting a helix or by binding lipid heads with an engineered tag, protein coverage above ~20% is sufficient to bend membranes. Consistent with this crowding mechanism, we find that even proteins unrelated to membrane curvature, such as green fluorescent protein (GFP), can bend membranes when sufficiently concentrated. These findings demonstrate a highly efficient mechanism by which the crowded protein environment on the surface of cellular membranes can contribute to membrane shape change.

Transition Path Sampling

Often, the dynamics of complex condensed materials is characterized by the presence of a wide range of different time scales, complicating the study of such processes with computer simulations. Consider, for instance, dynamical processes occurring in liquid water. Here, the fastest molecular processes are intramolecular vibrations with periods in the 10–20 fs range. The translational and rotational motions of water molecules occur on a significantly longer time scale. Typically, the direction of translational motion of a molecule persist for about 500 fs, corresponding to 50 vibrational periods. Hydrogen bonds, responsible for many of the unique properties of liquid water, have an average lifetime of about 1 ps and the rotational motion of water molecules stays correlated for about 10 ps. Much longer time scales are typically involved if covalent bonds are broken and formed. For instance, the average lifetime of a water molecule in liquid water before it dissociates and forms hydroxide and hydronium ions is on the order of 10 h. This enormous range of time scales, spanning nearly 20 orders of magnitude, is a challenge for the computer simulator who wants to study such processes.

Equilibrium fluctuations of a single folded protein reveal a multitude of potential cryptic allosteric sites

Cryptic allosteric sites—transient pockets in a folded protein that are invisible to conventional experiments but can alter enzymatic activity via allosteric communication with the active site—are a promising opportunity for facilitating drug design by greatly expanding the repertoire of available drug targets. Unfortunately, identifying these sites is difficult, typically requiring resource-intensive screening of large libraries of small molecules. Here, we demonstrate that Markov state models built from extensive computer simulations (totaling hundreds of microseconds of dynamics) can identify prospective cryptic sites from the equilibrium fluctuations of three medically relevant proteins—β-lactamase, interleukin-2, and RNase H—even in the absence of any ligand. As in previous studies, our methods reveal a surprising variety of conformations—including bound-like configurations—that implies a role for conformational selection in ligand binding. Moreover, our analyses lead to a number of unique insights. First, direct comparison of simulations with and without the ligand reveals that there is still an important role for an induced fit during ligand binding to cryptic sites and suggests new conformations for docking. Second, correlations between amino acid sidechains can convey allosteric signals even in the absence of substantial backbone motions. Most importantly, our extensive sampling reveals a multitude of potential cryptic sites—consisting of transient pockets coupled to the active site—even in a single protein. Based on these observations, we propose that cryptic allosteric sites may be even more ubiquitous than previously thought and that our methods should be a valuable means of guiding the search for such sites.

Elucidating the mechanism of selective ion adsorption to the liquid water surface

Adsorption of aqueous thiocyanate ions from bulk solution to the liquid/vapor interface was measured as a function of temperature by resonant UV second harmonic generation spectroscopy. The resulting adsorption enthalpy and entropy changes of this prototypical chaotrope were both determined to be negative. This surprising result is supported by molecular simulations, which clarify the microscopic origins of observed thermodynamic changes. Calculations reveal energetic influences of adsorbed ions on their surroundings to be remarkably local. Negative adsorption enthalpies thus reflect a simple repartitioning of solvent density among surface, bulk, and coordination regions. A different, and much less spatially local, mechanism underlies the concomitant loss of entropy. Simulations indicate that ions at the interface can significantly bias surface height fluctuations even several molecular diameters away, imposing restrictions consistent with the scale of measured and computed adsorption entropies. Based on these results, we expect an ion’s position in the Hofmeister lyotropic series to be determined by a combination of driving forces associated with the pinning of capillary waves and with a competition between ion hydration energy and the neat liquid’s surface tension.

Direct Observation of Nanoparticle Superlattice Formation by Using Liquid Cell Transmission Electron Microscopy

Direct imaging of nanoparticle solutions by liquid phase transmission electron microscopy has enabled unique in situ studies of nanoparticle motion and growth. In the present work, we report on real-time formation of two-dimensional nanoparticle arrays in the very low diffusive limit, where nanoparticles are mainly driven by capillary forces and solvent fluctuations. We find that superlattice formation appears to be segregated into multiple regimes. Initially, the solvent front drags the nanoparticles, condensing them into an amorphous agglomerate. Subsequently, the nanoparticle crystallization into an array is driven by local fluctuations. Following the crystallization event, superlattice growth can also occur via the addition of individual nanoparticles drawn from outlying regions by different solvent fronts. The dragging mechanism is consistent with simulations based on a coarse-grained lattice gas model at the same limit.

Transition path sampling: throwing ropes over mountains in the dark

Understanding rare transitions occurring in complex systems, for instance chemical reactions in solution, poses the problem of finding and analysing the trajectories that move from one basin of attraction to another on a complicated potential energy surface. We have developed a systematic approach for finding these trajectories using computer simulations without preconceived knowledge of transition states. The approach follows from a novel statistical mechanics and thermodynamics of trajectories and has been demonstrated with several applications.

Impact of Assembly State on the Defect Tolerance of TMV-Based Light Harvesting Arrays

Self-assembling, light harvesting arrays of organic chromophores can be templated using the tobacco mosaic virus coat protein (TMVP). The efficiency of energy transfer within systems containing a high ratio of donors to acceptors shows a strong dependence on the TMVP assembly state. Rod and disk assemblies derived from a single stock of chromophore-labeled protein exhibit drastically different levels of energy transfer, with rods significantly outperforming disks. The origin of the superior transfer efficiency was probed through the controlled introduction of photoinactive conjugates into the assemblies. The efficiency of the rods showed a linear dependence on the proportion of deactivated chromophores, suggesting the availability of redundant energy transfer pathways that can circumvent defect sites. Similar disk-based systems were markedly less efficient at all defect levels. To examine these differences further, the brightness of donor-only systems was measured as a function of defect incorporation. In rod assemblies, the photophysical properties of the donor chromophores showed a significant dependence on the number of defects. These differences can be partly attributed to vertical energy transfer events in rods that occur more rapidly than the horizontal transfers in disks. Using these geometries and the previously measured energy transfer rates, computational models were developed to understand this behavior in more detail and to guide the optimization of future systems. These simulations have revealed that significant differences in excited state dissipation rates likely also contribute to the greater efficiency of the rods and that statistical variations in the assembly process play a more minor role.

Probing the Conformational Distributions of Subpersistence Length DNA

We have measured the bending elasticity of short double-stranded DNA (dsDNA) chains through small-angle x-ray scattering from solutions of dsDNA-linked dimers of gold nanoparticles. This method, which does not require exertion of external forces or binding to a substrate, reports on the equilibrium distribution of bending fluctuations, not just an average value (as in ensemble fluorescence resonance energy transfer) or an extreme value (as in cyclization), and in principle provides a more robust data set for assessing the suitability of theoretical models. Our experimental results for dsDNA comprising 42-94 basepairs are consistent with a simple wormlike chain model of dsDNA elasticity, whose behavior we have determined from Monte Carlo simulations that explicitly represent nanoparticles and their alkane tethers. A persistence length of 50 nm (150 basepairs) gave a favorable comparison, consistent with the results of single-molecule force-extension experiments on much longer dsDNA chains, but in contrast to recent suggestions of enhanced flexibility at these length scales.