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.

Emergent Sequence Biasing in Step-Growth Copolymerization: Influence of Non-Bonded Interactions and Comonomer Reactivities.

The phase behavior and material properties of copolymers are intrinsically dependent on their primary comonomer sequences. Achieving precise control over monomer sequence in synthetic copolymerizations is challenging, as sequence determination is influenced not only by the reaction conditions and the properties of the reactants but also by the statistical nature of the copolymerization process itself. Mayo-Lewis reactivity ratios are often used to predict copolymer composition and sequence and are based on ratios of static reactivity constants. However, prior results have demonstrated that in a generic, solution-based step-growth A,B-copolymerization, relatively weak non-bonded attractions between certain monomer pairs induce emergent microphase separations. Such polymerization-driven separations lead to deviations from standard kinetics due to the emergent heterogeneities in reactant concentrations, which can also cause significant shifts in the resulting copolymer sequences. Previously, these effects were observed in systems where the activation energies were equal for all reaction pathways, that is, between all monomer pair combinations. In this work, we explore the combined effects on copolymerization kinetics of differences in both activation energies and non-bonded attractions between monomers and examine the sequences produced within this same step-growth copolymerization model. Our results indicate that altering activation energies influences the kinetics and sequences in a manner that also depends on the non-bonded attractions, showing that these effects may work in concert or in opposition to one another to bias the sequences formed. Non-standard kinetic behaviors and long-range sequence biasing are observed under certain conditions, and the extent of each clearly shifts as the reaction proceeds. These findings provide insight into the complex interplay between sequence and nascent oligomer phase behavior, highlighting the potential for exploiting emergent phase properties in the informed design of advanced sequence-biased materials.

Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove.

Advanced carbon microelectrodes, including many carbon-nanotube (CNT)-based electrodes, are being developed for the in vivo detection of neurotransmitters such as dopamine (DA). Our prior simulations of DA and dopamine-o-quinone (DOQ) on pristine, flat graphene showed rapid surface diffusion for all adsorbed species, but it is not known how CNT surfaces affect dopamine adsorption and surface diffusivity. In this work, we use molecular dynamics simulations to investigate the adsorbed structures and surface diffusion dynamics of DA and DOQ on CNTs of varying curvature and helicity. In addition, we study DA dynamics in a groove between two aligned CNTs to model the spatial constraints at the junctions within CNT assemblies. We find that the adsorbate diffusion on a solvated CNT surface depends upon curvature. However, this effect cannot be attributed to changes in the surface energy roughness because the lateral distributions of the molecular adsorbates are similar across curvatures, diffusivities on zigzag and armchair CNTs are indistinguishable, and the curvature dependence disappears in the absence of solvent. Instead, adsorbate diffusivities correlate with the vertical placement of the adsorbate's moieties, its tilt angle, its orientation along the CNT axis, and the number of waters in its first hydration shell, all of which will influence its effective hydrodynamic radius. Finally, DA diffuses into and remains in the groove between a pair of aligned and solvated CNTs, enhancing diffusivity along the CNT axis. These first studies of surface diffusion on a CNT electrode surface are important for understanding the changes in diffusion dynamics of dopamine on nanostructured carbon electrode surfaces.

Atomistic Simulations of Dopamine Diffusion Dynamics on a Pristine Graphene Surface.

Carbon microelectrodes enable in vivo detection of neurotransmitters, and new electrodes aim to optimize the carbon surface. However, atomistic detail on the diffusion and orientation of neurotransmitters near these surfaces is lacking. Here, we employ molecular dynamics simulations to investigate the surface diffusion of dopamine (DA), its oxidation product dopamine-o-quinone (DOQ), and their protonated forms on the pristine basal plane of flat graphene. We find that all DA species rapidly adsorb to the surface and remain adsorbed, even without a holding potential or graphene surface defects. We also find that the diffusivities of the adsorbed and the fully solvated DA are similar and that the protonated species diffuse more slowly on the surface than their corresponding neutral forms, while the oxidized species diffuse more rapidly. Structurally, we find that the underlying graphene lattice has little influence over the molecular adsorbate's lateral position, and the vertical placement of the amine group on dopamine is highly dependent upon its charge. Finally, we find that solvation has a large effect on surface diffusivities. These first results from molecular dynamics simulations of dopamine at the aqueous-graphene interface show that dopamine diffuses rapidly on the surface, even without an applied potential, and provide a basis for future simulations of neurotransmitter structure and dynamics on advanced carbon materials electrodes.

Selective solvent conditions influence sequence development and supramolecular assembly in step-growth copolymerization.

Sequence control in synthetic copolymers remains a tantalizing objective in polymer science due to the influence of sequence on material properties and self-organization. A greater understanding of sequence development throughout the polymerization process will aid the design of simple, generalizable methods to control sequence and tune supramolecular assembly. In previous simulations of solution-based step-growth copolymerizations, we have shown that weak, non-bonding attractions between monomers of the same type can produce a microphase separation among the lengthening nascent oligomers and thereby alter sequence. This work explores the phenomenon further, examining how effective attractive interactions, mediated by a solvent selective for one of the reacting species, impact the development of sequence and the supramolecular assembly in a simple A-B copolymerization. We find that as the effective attractions between monomers increase, an emergent self-organization of the reactants causes a shift in reaction kinetics and sequence development. When the solvent-mediated interactions are selective enough, the simple mixture of A and B monomers oligomerize and self-assemble into structures characteristic of amphiphilic copolymers. The composition and morphology of these structures and the sequences of their chains are sensitive to the relative balance of affinities between the comonomer species. Our results demonstrate the impact of differing A-B monomer-solvent affinities on sequence development in solution-based copolymerizations and are of consequence to the informed design of synthetic methods for sequence controlled amphiphilic copolymers and their aggregates.

The Sequence of a Step-Growth Copolymer Can Be Influenced by Its Own Persistence Length.

Synthetic copolymer sequences remain challenging to control, and there are features of even simple one-pot, solution-based copolymerizations that are not yet fully understood. In previous simulations on step-growth copolymerizations in solution, we demonstrated that modest variations in the attractions between type A and B monomers could significantly influence copolymer sequence through an emergent aggregation and phase separation initiated by the lengthening of nascent oligomers. Here we investigate how one aspect of a copolymer's geometry-its flexibility-can modulate those effects. Our simulations show the onset of strand alignment within the polymerization-induced aggregates as chain stiffness increases and demonstrate that this alignment can influence the resulting copolymer sequences. For less flexible copolymers, with persistence lengths ≥10 monomers, modest nonbonded attractions of ∼kBT between monomers of the same type yield A and B blocks of a characteristic length and result in a polydispersity index that grows rapidly, peaks, and then diminishes as the reaction proceeds. These results demonstrate that for copolymer systems with modest variations in intermonomer attractions and physically realistic flexibilities a nascent copolymer's persistence length can influence its own sequence.

Evidence for the Supramolecular Organization of a Bacterial Outer-Membrane Protein from In Vivo Pulse Electron Paramagnetic Resonance Spectroscopy.

In the outer membrane of Gram-negative bacteria, membrane proteins are thought to be organized into domains or islands that play a role in the segregation, movement, and turnover of membrane components. However, there is presently limited information on the structure of these domains or the molecular interactions that mediate domain formation. In the present work, the Escherichia coli outer membrane vitamin B12 transporter, BtuB, was spin-labeled, and double electron-electron resonance was used to measure the distances between proteins in intact cells. These data together with Monte Carlo simulations provide evidence for the presence of specific intermolecular contacts between BtuB monomers that could drive the formation of string-like oligomers. Moreover, the EPR data provide evidence for the location of the interacting interfaces and indicate that lipopolysaccharide mediates the contacts between BtuB monomers.

Predicting the effect of chain-length mismatch on phase separation in noble metal nanoparticle monolayers with chemically mismatched ligands.

Nanoparticles (NPs) protected with a ligand monolayer hold promise for a wide variety of applications, from photonics and catalysis to drug delivery and biosensing. Monolayers that include a mixture of ligand types can have multiple chemical functionalities and may also self-assemble into advantageous patterns. Previous work has shown that both chemical and length mismatches among these surface ligands influence phase separation. In this work, we examine the interplay between these driving forces, first by using our previously-developed configurationally-biased Monte Carlo (CBMC) algorithm to predict, then by using our matrix assisted laser desorption/ionization mass spectrometry (MALDI-MS) technique to experimentally probe, the surface morphologies of a series of two-ligand mixtures on the surfaces of ultrasmall silver NPs. Specifically, we examine three such mixtures, each of which has the same chemical mismatch (consisting of a hydrophobic alkanethiol and a hydrophilic mercapto-alcohol), but varying degrees of chain-length mismatch. This delicate balance between chemical and length mismatches provides a challenging test for our CBMC prediction algorithm. Even so, the simulations are able to quantitatively predict the MALDI-MS results for all three ligand mixtures, while also providing atomic-scale details from the equilibrated ligand structures, such as patch sizes and co-crystallization patterns. The resulting monolayer morphologies range from randomly-mixed to Janus-like, demonstrating that chain-length modifications are an effective way to tune monolayer morphology without needing to alter chemical functionalities.

Computational and Experimental Investigation of Janus-like Monolayers on Ultrasmall Noble Metal Nanoparticles.

Detection of monolayer morphology on nanoparticles smaller than 10 nm has proven difficult with traditional visualization techniques. Here matrix-assisted laser desorption ionization mass spectrometry (MALDI-MS) is used in conjunction with atomistic simulations to detect the formation of Janus-like monolayers on noble metal nanoparticles. Silver metal nanoparticles were synthesized with a monolayer consisting of dodecanethiol (DDT) and mercaptoethanol (ME) at varying ratios. The nanoparticles were then analyzed using MALDI-MS, which gives information on the local ordering of ligands on the surface. The MALDI-MS analysis showed large deviations from random ordering, suggesting phase separation of the DDT/ME monolayers. Atomistic Monte Carlo (MC) calculations were then used to simulate the nanoscale morphology of the DDT/ME monolayers. In order to quantitatively compare the computational and experimental results, we developed a method for determining an expected MALDI-MS spectrum from the atomistic simulation. Experiments and simulations show quantitative agreement, and both indicate that the DDT/ME ligands undergo phase separation, resulting in Janus-like nanoparticle monolayers with large, patchy domains.

A Predictive Approach for the Optical Control of Carbonic Anhydrase II Activity.

Optogenetics and photopharmacology are powerful approaches to investigating biochemical systems. While the former is based on genetically encoded photoreceptors that utilize abundant chromophores, the latter relies on synthetic photoswitches that are either freely diffusible or covalently attached to specific bioconjugation sites, which are often native or engineered cysteines. The identification of suitable cysteine sites and appropriate linkers for attachment is generally a lengthy and cumbersome process. Herein, we describe an in silico screening approach that is designed to propose a small number of optimal combinations. By applying this computational approach to human carbonic anhydrase and a set of three photochromic tethered ligands, the number of potential site-ligand combinations was narrowed from over 750 down to 6, which we then evaluated experimentally. Two of these six combinations resulted in light-responsive human Carbonic Anhydrases (LihCAs), which were characterized with enzymatic activity assays, mass spectrometry, and X-ray crystallography. Our study also provides insights into the reactivity of cysteines toward maleimides and the hydrolytic stability of the adducts obtained.

Fluctuations within folded proteins: implications for thermodynamic and allosteric regulation.

Folded protein structures are both stable and dynamic. Historically, our clearest window into these structures came from X-ray crystallography, which generally provided a static image of each protein's singular "folded state", highlighting its stability. Deviations away from that crystallographic structure were difficult to quantify, and as a result, their potential functional consequences were often neglected. However, several dynamical and statistical studies now highlight the structural variability that is present within the protein's folded state. Here we review mounting evidence of the importance of these structural rearrangements; both experiment and computation indicate that folded proteins undergo substantial fluctuations that can greatly influence their function. Crucially, recent studies have shown that structural elements of proteins, especially their side-chain degrees of freedom, fluctuate in ways that generate significant conformational heterogeneity. The entropy associated with these motions contributes to the folded structure's thermodynamic stability. In addition, since these fluctuations can shift in response to perturbations such as ligand binding, they may play an important role in the protein's capacity to respond to environmental cues. In one compelling example, the entropy associated with side-chain fluctuations contributes significantly to regulating the binding of calmodulin to a set of peptide ligands. The neglect of fluctuations within proteins' native states was often justified by the dense packing within folded proteins, which has inspired comparisons with crystalline solids. Many liquids, however, can achieve similarly dense packing yet fluidity is maintained through correlated molecular motions. Indeed, the studies we discuss favor comparison of folded proteins not with solids but instead with dense liquids, where the internal side chain fluidity is facilitated by collective motions that are correlated over long distances. These correlated rearrangements can enable allosteric communication between different parts of a protein, through subtle and varied channels. Such long-range correlations appear to be an innate feature of proteins in general, manifest even in molecules lacking known allosteric regulators and arising robustly from the physical nature of their internal environment. Given their ubiquity, it is only to be expected that, over time, nature has refined some subset of these correlated motions and put them to use. Native state fluctuations increasingly appear to be vital for proteins' natural functions. Understanding the diversity, origin, and range of these rearrangements may provide novel routes for rationally manipulating biomolecular activity.

A first-principles polarized Raman method for determining whether a uniform region of a sample is crystalline or isotropic.

Previous methods for determining whether a uniform region of a sample is crystalline or isotropic-what we call the "state of internal orientation" S-require a priori knowledge of properties of the purely crystalline and purely isotropic states. In addition, these methods can be ambiguous in their determination of state S for particular materials and, for a given material, the spectral methods can be ambiguous when using particular peaks. Using first-principles Raman theory, we have discovered a simple, non-resonance, polarized Raman method for determining the state S that requires no information a priori and will work unambiguously for any material using any vibrational mode. Similar to the concept behind "magic angle spinning" in NMR, we have found that for a special set of incident/analyzed polarizations and scattering angle, the dependence of the Raman modulation depth M on the sample composition-and, for crystalline regions, the unit cell orientation-falls out completely, leaving dependence on only whether the region is crystalline (M = 1) or isotropic (M = 0). Further, upon scanning between homogeneous regions or domains within a heterogeneous sample, our signal M is a clear detector of the region boundaries, so that when combined with methods for determining the orientations of the crystalline domains, our method can be used to completely characterize the molecular structure of an entire heterogeneous sample to a very high certainty. Interestingly, our method can also be used to determine when a given mode is vibrationally degenerate. While simulations on realistic terthiophene systems are included to illustrate our findings, our method should apply to any type of material, including thin films, molecular crystals, and semiconductors. Finally, our discovery of these relationships required derivations of Raman intensity formulas that are at least as general as any we have found, and herein we present our comprehensive formulas for both the crystalline and isotropic states.

Impact of molecular symmetry on single-molecule conductance.

We have measured the single-molecule conductance of a family of bithiophene derivatives terminated with methyl sulfide gold-binding linkers using a scanning tunneling microscope based break-junction technique. We find a broad distribution in the single-molecule conductance of bithiophene compared with that of a methyl sulfide terminated biphenyl. Using a combination of experiments and calculations, we show that this increased breadth in the conductance distribution is explained by the difference in 5-fold symmetry of thiophene rings as compared to the 6-fold symmetry of benzene rings. The reduced symmetry of thiophene rings results in a restriction on the torsion angle space available to these molecules when bound between two metal electrodes in a junction, causing each molecular junction to sample a different set of conformers in the conductance measurements. In contrast, the rotations of biphenyl are essentially unimpeded by junction binding, allowing each molecular junction to sample similar conformers. This work demonstrates that the conductance of bithiophene displays a strong dependence on the conformational fluctuations accessible within a given junction configuration, and that the symmetry of such small molecules can significantly influence their conductance behaviors.

Polarized Raman spectroscopy of oligothiophene crystals to determine unit cell orientation.

Raman spectra were recorded experimentally and calculated theoretically for bithiophene, terthiophene, and quaterthiophene samples as a function of excitation polarization. Distinct spectral signatures were assigned and correlated to the molecular/unit cell orientation as determined by X-ray diffraction. The ability to predict molecular/unit cell orientation within organic crystals using polarized Raman spectroscopy was evaluated by predicting the unit cell orientation in a simulated terthiophene crystal given a random set of simulated polarized Raman spectra. Polarized Raman spectroscopy offers a promising tool to quickly and economically determine the unit cell orientation in known organic crystals and crystalline thin films. Implications of our methodologies for studying individual molecule conformations are discussed.

Accurate Force Field Development for Modeling Conjugated Polymers.

The modeling of the conformational properties of conjugated polymers entails a unique challenge for classical force fields. Conjugation imposes strong constraints upon bond rotation. Planar configurations are favored, but the concomitantly shortened bond lengths result in moieties being brought into closer proximity than usual. The ensuing steric repulsions are particularly severe in the presence of side chains, straining angles, and stretching bonds to a degree infrequently found in nonconjugated systems. We herein demonstrate the resulting inaccuracies by comparing the LMP2-calculated inter-ring torsion potentials for a series of substituted stilbenes and bithiophenes to those calculated using standard classical force fields. We then implement adjustments to the OPLS-2005 force field in order to improve its ability to model such systems. Finally, we show the impact of these changes on the dihedral angle distributions, persistence lengths, and conjugation length distributions observed during molecular dynamics simulations of poly[2-methoxy-5-(2'-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV) and poly 3-hexylthiophene (P3HT), two of the most widely used conjugated polymers.

Long-range intra-protein communication can be transmitted by correlated side-chain fluctuations alone.

Allosteric regulation is a key component of cellular communication, but the way in which information is passed from one site to another within a folded protein is not often clear. While backbone motions have long been considered essential for long-range information conveyance, side-chain motions have rarely been considered. In this work, we demonstrate their potential utility using Monte Carlo sampling of side-chain torsional angles on a fixed backbone to quantify correlations amongst side-chain inter-rotameric motions. Results indicate that long-range correlations of side-chain fluctuations can arise independently from several different types of interactions: steric repulsions, implicit solvent interactions, or hydrogen bonding and salt-bridge interactions. These robust correlations persist across the entire protein (up to 60 Å in the case of calmodulin) and can propagate long-range changes in side-chain variability in response to single residue perturbations.

Controlling chain conformation in conjugated polymers using defect inclusion strategies.

The Horner method was used to synthesize random copolymers of poly(2-methoxy-5-(2'-ethylhexyloxy)-p-phenylene vinylene) (MEH-PPV) that incorporated different backbone-directing monomers. Single-molecule polarization absorption studies of these new polymers demonstrate that defects that preserve the linear backbone of PPV-type polymers assume the highly anisotropic configurations found in defect-free MEH-PPV. Rigid defects that are bent lower the anisotropy of the single chain, and saturated defects that provide rotational freedom for the chain backbone allow for a wide variety of possible configurations. Molecular dynamics simulations of model defect PPV oligomers in solution demonstrate that defect-free and linearly defected oligomers remain extended while the bent and saturated defects tend toward more folded, compact structures.

Calculation of proteins' total side-chain torsional entropy and its influence on protein-ligand interactions.

Despite the high density within a typical protein fold, the ensemble of sterically permissible side-chain repackings is vast. Here, we examine the extent of this variability that survives energetic biases due to van der Waals interactions, hydrogen bonding, salt bridges, and solvation. Monte Carlo simulations of an atomistic model exhibit thermal fluctuations among a diverse set of side-chain arrangements, even with the peptide backbone fixed in its crystallographic conformation. We have quantified the torsional entropy of this native-state ensemble, relative to that of a noninteracting reference system, for 12 small proteins. The reduction in entropy per rotatable bond due to each kind of interaction is remarkably consistent across this set of molecules. To assess the biophysical importance of these fluctuations, we have estimated side-chain entropy contributions to the binding affinity of several peptide ligands with calmodulin. Calculations for our fixed-backbone model correlate very well with experimentally determined binding entropies over a range spanning more than 80 kJ/(mol x 308 K).