Combining particle and field-theoretic polymer models with multi-representation simulations.

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.

Efficient Synthesis of Asymmetric Miktoarm Star Polymers.

Asymmetric miktoarm star polymers comprising an unequal number of chemically-distinct blocks connected at a common junction produce unique material properties, yet existing synthetic strategies are beleaguered by complicated reaction schemes that are restricted in both monomer scope and yield. Here, we introduce a new synthetic approach coined "µSTAR" - Miktoarm Synthesis by Termination After Ring-opening metathesis polymerization - that circumvents these traditional synthetic limitations by constructing the block-block junction in a scalable, one-pot process involving (1) grafting-through polymerization of a macromonomer followed by (2) in-situ enyne-mediated termination to install a single mikto-arm with exceptional efficiency. This modular µSTAR platform cleanly generates AB n and A(BA') n miktoarm star polymers with unprecedented versatility in the selection of A and B chemistries as demonstrated using many common polymer building blocks: poly(siloxane), poly(acrylate), poly(methacrylate), poly(ether), poly(ester), and poly(styrene). The average number of B or BA' arms (n) is easily controlled by the molar equivalents of macromonomer relative to Grubbs catalyst in the initial ring-opening metathesis polymerization step. While these materials are characterized by dispersity in n that arises from polymerization statistics, they self-assemble into mesophases that are identical to those predicted for precise miktoarm stars as evidenced by small-angle X-ray scattering experiments and self-consistent field theory simulations. In summary, the µSTAR technique provides a significant boost in design flexibility and synthetic simplicity while retaining the salient phase behavior of precise miktoarm star materials.

Complete Photonic Band Gaps with Nonfrustrated ABC Bottlebrush Block Polymers.

Bottlebrush block polymers are a promising platform for self-assembled photonic materials, yet most work has been limited to one-dimensional photonic crystals based on the lamellar phase. Here we demonstrate with simulation that nonfrustrated ABC bottlebrush block polymers can be used to self-assemble three-dimensional photonic crystals with complete photonic band gaps. To show this, we have developed a computational approach that couples self-consistent field theory (SCFT) simulations to Maxwell's equations, thereby permitting a direct link between molecular design, self-assembly, and photonic band structures. Using this approach, we calculate the phase diagram of nonfrustrated ABC bottlebrush block polymers and identify regions where the alternating gyroid and alternating diamond phases are stable. By computing the photonic band structures of these phases, we demonstrate that complete band gaps can be found in regions of thermodynamic stability, thereby suggesting a route to realize these photonic materials experimentally. Furthermore, we demonstrate that gap size depends on volume fraction, segregation strength, and polymer architecture, and we identify a design strategy based on symmetry breaking that can achieve band gaps for lower values of refractive index contrast. Taken together, the approach presented here provides a powerful and flexible tool for predicting both the self-assembly and photonic band structures of polymeric materials.

Architecture Effects in Complex Spherical Assemblies of (AB)n-Type Block Copolymers.

Molecular architecture plays a key role in the self-assembly of block copolymers, but few studies have systematically examined the influence of chain connectivity on tetrahedrally close-packed (TCP) sphere phases. Here, we report a versatile material platform comprising two blocks with substantial conformational asymmetry, A = poly(trifluoroethyl acrylate) and B = poly(dodecyl acrylate), and use it to compare the phase behavior of AB diblocks, ABA triblocks, and (AB)n radial star copolymers with n = 3 or 4. Each architecture forms TCP sphere phases at minority A block compositions (fA < 0.5), namely, σ and A15, but with differences in the location of order-order phase boundaries that are not anticipated by mean-field self-consistent field theory simulations. These results expand the palette of polymer architectures that readily self-assemble into complex TCP structures and suggest important design considerations when targeting specific phases of interest.

Deep learning for automated classification and characterization of amorphous materials.

It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it difficult to define structural metrics. In this work, we apply deep learning algorithms to accurately classify amorphous materials and characterize their structural features. Specifically, we show that convolutional neural networks and message passing neural networks can classify two-dimensional liquids and liquid-cooled glasses from molecular dynamics simulations with greater than 0.98 AUC, with no a priori assumptions about local particle relationships, even when the liquids and glasses are prepared at the same inherent structure energy. Furthermore, we demonstrate that message passing neural networks surpass convolutional neural networks in this context in both accuracy and interpretability. We extract a clear interpretation of how message passing neural networks evaluate liquid and glass structures by using a self-attention mechanism. Using this interpretation, we derive three novel structural metrics that accurately characterize glass formation. The methods presented here provide a procedure to identify important structural features in materials that could be missed by standard techniques and give unique insight into how these neural networks process data.

Stability of the A15 phase in diblock copolymer melts.

The self-assembly of block polymers into well-ordered nanostructures underpins their utility across fundamental and applied polymer science, yet only a handful of equilibrium morphologies are known with the simplest AB-type materials. Here, we report the discovery of the A15 sphere phase in single-component diblock copolymer melts comprising poly(dodecyl acrylate)-block-poly(lactide). A systematic exploration of phase space revealed that A15 forms across a substantial range of minority lactide block volume fractions (fL = 0.25 - 0.33) situated between the σ-sphere phase and hexagonally close-packed cylinders. Self-consistent field theory rationalizes the thermodynamic stability of A15 as a consequence of extreme conformational asymmetry. The experimentally observed A15-disorder phase transition is not captured using mean-field approximations but instead arises due to composition fluctuations as evidenced by fully fluctuating field-theoretic simulations. This combination of experiments and field-theoretic simulations provides rational design rules that can be used to generate unique, polymer-based mesophases through self-assembly.

1CPN: A coarse-grained multi-scale model of chromatin.

A central question in epigenetics is how histone modifications influence the 3D structure of eukaryotic genomes and, ultimately, how this 3D structure is manifested in gene expression. The wide range of length scales that influence the 3D genome structure presents important challenges; epigenetic modifications to histones occur on scales of angstroms, yet the resulting effects of these modifications on genome structure can span micrometers. There is a scarcity of computational tools capable of providing a mechanistic picture of how molecular information from individual histones is propagated up to large regions of the genome. In this work, a new molecular model of chromatin is presented that provides such a picture. This new model, referred to as 1CPN, is structured around a rigorous multiscale approach, whereby free energies from an established and extensively validated model of the nucleosome are mapped onto a reduced coarse-grained topology. As such, 1CPN incorporates detailed physics from the nucleosome, such as histone modifications and DNA sequence, while maintaining the computational efficiency that is required to permit kilobase-scale simulations of genomic DNA. The 1CPN model reproduces the free energies and dynamics of both single nucleosomes and short chromatin fibers, and it is shown to be compatible with recently developed models of the linker histone. It is applied here to examine the effects of the linker DNA on the free energies of chromatin assembly and to demonstrate that these free energies are strongly dependent on the linker DNA length, pitch, and even DNA sequence. The 1CPN model is implemented in the LAMMPS simulation package and is distributed freely for public use.

The Free Energy Landscape of Internucleosome Interactions and Its Relation to Chromatin Fiber Structure.

The supramolecular chromatin fiber is governed by molecular scale energetics and interactions. Such energetics originate from the fiber's building block, the nucleosome core particle (NCP). In recent years, the chromatin fiber has been examined through perturbative methods in attempts to extract the energetics of nucleosome association in the fiber. This body of work has led to different results from experiments and simulations concerning the nucleosome-nucleosome energetics. Here, we expand on previous experiments and use coarse-grained simulations to evaluate the energetics inherent to nucleosomes across a variety of parameters in configurational and environmental space. Through this effort, we are able to uncover molecular processes that are critical to understanding the 30 nm chromatin fiber structure. In particular, we describe the NCP-NCP interactions by relying on an anisotropic energetic landscape, rather than a single potential energy value. The attractions in that landscape arise predominantly from the highly anisotropic interactions provided by the NCP histone N-terminal domain (NTD) tails. Our results are found to be in good agreement with recent nucleosome interaction experiments that suggest a maximum interaction energy of 2.69k B T. Furthermore, we examine the influence of crucial epigenetic modifications, such as acetylation of the H4 tail, and how they modify the underlying landscape. Our results for acetylated NCP interactions are also in agreement with experiment. We additionally find an induced chirality in NCP-NCP interactions upon acetylation that reduces interactions which would correspond to a left-handed superhelical chromatin fiber.

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.

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.

In silico evidence for sequence-dependent nucleosome sliding.

Nucleosomes represent the basic building block of chromatin and provide an important mechanism by which cellular processes are controlled. The locations of nucleosomes across the genome are not random but instead depend on both the underlying DNA sequence and the dynamic action of other proteins within the nucleus. These processes are central to cellular function, and the molecular details of the interplay between DNA sequence and nucleosome dynamics remain poorly understood. In this work, we investigate this interplay in detail by relying on a molecular model, which permits development of a comprehensive picture of the underlying free energy surfaces and the corresponding dynamics of nucleosome repositioning. The mechanism of nucleosome repositioning is shown to be strongly linked to DNA sequence and directly related to the binding energy of a given DNA sequence to the histone core. It is also demonstrated that chromatin remodelers can override DNA-sequence preferences by exerting torque, and the histone H4 tail is then identified as a key component by which DNA-sequence, histone modifications, and chromatin remodelers could in fact be coupled.

A Molecular View of the Dynamics of dsDNA Packing Inside Viral Capsids in the Presence of Ions.

Genome packing in viruses and prokaryotes relies on positively charged ions to reduce electrostatic repulsions, and induce attractions that can facilitate DNA condensation. Here we present molecular dynamics simulations spanning several microseconds of dsDNA packing inside nanometer-sized viral capsids. We use a detailed molecular model of DNA that accounts for molecular structure, basepairing, and explicit counterions. The size and shape of the capsids studied here are based on the 30-nanometer-diameter gene transfer agents of bacterium Rhodobacter capsulatus that transfer random 4.5-kbp (1.5 µm) DNA segments between bacterial cells. Multivalent cations such as spermidine and magnesium induce attraction between packaged DNA sites that can lead to DNA condensation. At high concentrations of spermidine, this condensation significantly increases the shear stresses on the packaged DNA while also reducing the pressure inside the capsid. These effects result in an increase in the packing velocity and the total amount of DNA that can be packaged inside the nanometer-sized capsids. In the simulation results presented here, high concentrations of spermidine3+ did not produce the premature stalling observed in experiments. However, a small increase in the heterogeneity of packing velocities was observed in the systems with magnesium and spermidine ions compared to the system with only salt. The results presented here indicate that the effect of multivalent cations and of spermidine, in particular, on the dynamics of DNA packing, increases with decreasing packing velocities.

Mechanical Response of DNA-Nanoparticle Crystals to Controlled Deformation.

The self-assembly of DNA-conjugated nanoparticles represents a promising avenue toward the design of engineered hierarchical materials. By using DNA to encode nanoscale interactions, macroscale crystals can be formed with mechanical properties that can, at least in principle, be tuned. Here we present in silico evidence that the mechanical response of these assemblies can indeed be controlled, and that subtle modifications of the linking DNA sequences can change the Young's modulus from 97 kPa to 2.1 MPa. We rely on a detailed molecular model to quantify the energetics of DNA-nanoparticle assembly and demonstrate that the mechanical response is governed by entropic, rather than enthalpic, contributions and that the response of the entire network can be estimated from the elastic properties of an individual nanoparticle. The results here provide a first step toward the mechanical characterization of DNA-nanoparticle assemblies, and suggest the possibility of mechanical metamaterials constructed using DNA.

Tension-Dependent Free Energies of Nucleosome Unwrapping.

Nucleosomes form the basic unit of compaction within eukaryotic genomes, and their locations represent an important, yet poorly understood, mechanism of genetic regulation. Quantifying the strength of interactions within the nucleosome is a central problem in biophysics and is critical to understanding how nucleosome positions influence gene expression. By comparing to single-molecule experiments, we demonstrate that a coarse-grained molecular model of the nucleosome can reproduce key aspects of nucleosome unwrapping. Using detailed simulations of DNA and histone proteins, we calculate the tension-dependent free energy surface corresponding to the unwrapping process. The model reproduces quantitatively the forces required to unwrap the nucleosome and reveals the role played by electrostatic interactions during this process. We then demonstrate that histone modifications and DNA sequence can have significant effects on the energies of nucleosome formation. Most notably, we show that histone tails contribute asymmetrically to the stability of the outer and inner turn of nucleosomal DNA and that depending on which histone tails are modified, the tension-dependent response is modulated differently.

A molecular view of DNA-conjugated nanoparticle association energies.

Nanoparticles functionalized with short sequences of DNA represent a promising platform for customizable self assembly. Though much recent research has focused on the phase behavior and assembly of these structures, little has been done to precisely characterize the pairwise interaction between particles. Here we present a detailed calculation of the association between DNA-nanoparticle conjugates using 3SPN.2, a coarse-grained model of DNA that accounts for molecular structure and base-pairing. We compare our results to those obtained experimentally using µm sized particles and analyze the free energy surfaces that characterize interparticle hybridization. Next, we study the importance of three-body effects and their impact on particle association and melting. Lastly, we explore the observation by Park et al. [Nature, 451, 553 (2008)] that DNA-nanoparticle crystallization can be inhibited by the deletion of a single nucleotide. Using our model, we suggest that the role of this nucleotide is to disrupt frustration.

DNA shape dominates sequence affinity in nucleosome formation.

Nucleosomes provide the basic unit of compaction in eukaryotic genomes, and the mechanisms that dictate their position at specific locations along a DNA sequence are of central importance to genetics. In this Letter, we employ molecular models of DNA and proteins to elucidate various aspects of nucleosome positioning. In particular, we show how DNA's histone affinity is encoded in its sequence-dependent shape, including subtle deviations from the ideal straight B-DNA form and local variations of minor groove width. By relying on high-precision simulations of the free energy of nucleosome complexes, we also demonstrate that, depending on DNA's intrinsic curvature, histone binding can be dominated by bending interactions or electrostatic interactions. More generally, the results presented here explain how sequence, manifested as the shape of the DNA molecule, dominates molecular recognition in the problem of nucleosome positioning.

Coarse-grained modeling of DNA curvature.

The interaction of DNA with proteins occurs over a wide range of length scales, and depends critically on its local structure. In particular, recent experimental work suggests that the intrinsic curvature of DNA plays a significant role on its protein-binding properties. In this work, we present a coarse grained model of DNA that is capable of describing base-pairing, hybridization, major and minor groove widths, and local curvature. The model represents an extension of the recently proposed 3SPN.2 description of DNA [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)], into which sequence-dependent shape and mechanical properties are incorporated. The proposed model is validated against experimental data including melting temperatures, local flexibilities, dsDNA persistence lengths, and minor groove width profiles.

Coarse-grained modeling of DNA oligomer hybridization: length, sequence, and salt effects.

A recently published coarse-grained DNA model [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)] is used to study the hybridization mechanism of DNA oligomers. Forward flux sampling is used to construct ensembles of reactive trajectories from which the effects of sequence, length, and ionic strength are revealed. Heterogeneous sequences are observed to hybridize via the canonical zippering mechanism. In contrast, homogeneous sequences hybridize through a slithering mechanism, while more complex base pair displacement processes are observed for repetitive sequences. In all cases, the formation of non-native base pairs leads to an increase in the observed hybridization rate constants beyond those observed in sequences where only native base pairs are permitted. The scaling of rate constants with length is captured by extending existing hybridization theories to account for the formation of non-native base pairs. Furthermore, that scaling is found to be similar for oligomeric and polymeric systems, suggesting that similar physics is involved.

Studying host cell protein interactions with monoclonal antibodies using high throughput protein A chromatography.

Protein A chromatography is typically used as the initial capture step in the purification of monoclonal antibodies produced in Chinese hamster ovary (CHO) cells. Although exploiting an affinity interaction for purification, the level of host cell proteins in the protein A eluent varies significantly with different feedstocks. Using a batch binding chromatography method, we performed a controlled study to assess host cell protein clearance across both MabSelect Sure and Prosep vA resins. We individually spiked 21 purified antibodies into null cell culture fluid generated with a non-producing cell line, creating mock cell culture fluids for each antibody with an identical composition of host cell proteins and antibody concentration. We demonstrated that antibody-host cell protein interactions are primarily responsible for the variable levels of host cell proteins in the protein A eluent for both resins when antibody is present. Using the additives guanidine HCl and sodium chloride, we demonstrated that antibody-host cell protein interactions may be disrupted, reducing the level of host cell proteins present after purification on both resins. The reduction in the level of host cell proteins differed between antibodies suggesting that the interaction likely varies between individual antibodies but encompasses both an electrostatic and hydrophobic component.

Computational modeling and analysis of insulin induced eukaryotic translation initiation.

Insulin, the primary hormone regulating the level of glucose in the bloodstream, modulates a variety of cellular and enzymatic processes in normal and diseased cells. Insulin signals are processed by a complex network of biochemical interactions which ultimately induce gene expression programs or other processes such as translation initiation. Surprisingly, despite the wealth of literature on insulin signaling, the relative importance of the components linking insulin with translation initiation remains unclear. We addressed this question by developing and interrogating a family of mathematical models of insulin induced translation initiation. The insulin network was modeled using mass-action kinetics within an ordinary differential equation (ODE) framework. A family of model parameters was estimated, starting from an initial best fit parameter set, using 24 experimental data sets taken from literature. The residual between model simulations and each of the experimental constraints were simultaneously minimized using multiobjective optimization. Interrogation of the model population, using sensitivity and robustness analysis, identified an insulin-dependent switch that controlled translation initiation. Our analysis suggested that without insulin, a balance between the pro-initiation activity of the GTP-binding protein Rheb and anti-initiation activity of PTEN controlled basal initiation. On the other hand, in the presence of insulin a combination of PI3K and Rheb activity controlled inducible initiation, where PI3K was only critical in the presence of insulin. Other well known regulatory mechanisms governing insulin action, for example IRS-1 negative feedback, modulated the relative importance of PI3K and Rheb but did not fundamentally change the signal flow.