©2017 by The DuBay Group. Proudly created with Wix.com.                                                                                                    Last Updated: March 2019

Research

Our research uses numerical simulations to investigate self-organization within complex environments. We are interested in how spatial and temporal variations influence the self-assembly processes for a variety of structures, ranging from copolymers to nanoparticle surfaces to viral capsids and other essential biomaterials.

Modeling the influence exerted by nascent oligomers on one another during step-growth copolymerizations

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Figure 1: Step-Growth Polymerizations. A schematic of the step-growth polymerization of a  blue and red copolymer. Each bead represents a monomer, and black lines connect monomers that are bound together.

Figure 2: Simulation Results of a Step-Growth A,B Copolymerization. We show here our results from simulations using the model above for an A (blue) and B (red) copolymer. A simple Lennard-Jones-like interaction (where repulsions are held fixed) exists between the type 1 particles within each bead, and the      ,      , and       values indicate the well-depth of the attractive portion of that non-bonded potential for each monomer combination. For (a), (b), and (c), snapshots are shown of the system after polymerization alongside the sequences of a sample of the resulting oligomers. The probabilities of neighboring monomers along the chain having the same identity,       , or the opposite identity,         , are also reported. In (a), there are equal attractions between all monomers, like and unlike; in (b), there are only attractions between like monomers; and in (c) there are only attractions between like monomers, but there is also an additional barrier of      for the reactions between like monomers. Steric repulsions and reaction barriers are otherwise fixed to be the same between all pairs. In (d),          is plotted vs. the reaction time for a series of simulations with different strengths of non-bonded attractions between like monomers (here      = 0). Finally, in (e), the phase behavior of non-reactive homo-oligomers of varying lengths (with half of the oligomers containing A monomers, and half containing B), with like attractions of varying strengths (again    = 0), is explored through the use of a visual assessment of chain structure (symbols) as well as the height of the first peak in the corresponding radial distribution functions for monomers not directly bound to one another (color-scale). See Zhang & DuBay 2019 [18].

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Copolymers are an essential and promising class of materials. However, synthetic copolymerizations are not yet able to achieve the degree of specificity in their sequences that can be found in biological copolymers such as proteins, where complex biochemical machinery ensures the precise placement of monomers in the chain. Current synthetic approaches to obtaining sequence-controlled copolymers are expensive and labor-intensive. To improve these efforts and gain a better understanding of the physics involved in sequence-determination, we are working to test the influence of non-bonded interactions, monomer geometries, and complex reaction environments on the sequences of step-grown copolymers through the use of coarse-grained simulations, while considering emergent collective behaviors among the polymerizing monomers, dimers, trimers, and nascent oligomers. Results from our investigations show that soft attractions among the nascent oligomers can significantly influence the final sequences of a set of copolymers. In addition, with only modest differences in attractions (on the order of    ) between different monomer pairs, a phase separation between segments enriched in on monomer or the other emerges as a result of the polymerization process itself. As a result, the sequence biasing we observe cannot be accounted for within conventional polymerization theories that assume that reactivity does not vary with polymer length (Zhang & DuBay [18]). In order to test our results in real polymerizations, we are currently collaborating with synthetic chemists at Southern Illinois University and Oak Ridge National Lab. This material is based upon work supported by the National Science Foundation under a CAREER Award – Grant No. 1848009.

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Computational investigations of oligomer phase separation on the faceted surface of a nanoparticle

Figure 3: Comparison of Ligand Fragment Distributions from MALDI-MS and Atomistic Simulations. The two measures show an excellent agreement and clear evidence of phase separation for a mixture of dodecanethiol (DDT) and mercaptoethanol (ME) ligands on the surface of ultrasmall silver NPs (Merz 2018 [16]).

Nanoparticles (NPs) coated with oligomer monolayers are currently being investigated for a wide range of applications, from advanced drug delivery to radiotherapies to protein sensing. When these surface monolayers are composed of different ligands, complex morphologies can emerge from partial or complete phase separations. These morphologies can significantly enhance NP functionality. However, characterizing the ligand morphologies on the surfaces of NPs has proven quite difficult, and traditional visualization techniques have run into problems. Prof. David Green, in UVa's School of Engineering and Applied Science, has developed a MALDI-MS characterization technique, but it is not able to provide atomistic-level details on the ligand morphologies. Thus, we have implemented an advanced Monte Carlo algorithm designed to enable the convergence to equilibrium within polymer brush systems in order to determine the atomistic-scale details of oligomer monolayers with two types of ligands on the surfaces of nanoparticles. We have now successfully reproduced or predicted the phase behavior, as reported by MALDI-MS data, for three ligand-ligand combinations, ( Merz 2018 [16], Merz 2019 [17]), and we are now working to systematically extend our study of ligand pairs – both in terms of the range of interactions represented and in terms of the chemistry made possible by certain ligand pairs. This material is based upon work supported by the National Science Foundation under Grant No. 1904884.

Modeling self-assembly within a time-variant environment

Many essential cellular processes depend on the ability of biostructures to self-organize, rearrange, and fall apart at precise locations in space and time. The environment within which they do so is exceedingly complex – the numerous molecules that mediate interactions between self-organizing components have concentrations that vary from one location to another, while also changing in time. We are currently using an established 2D model of viral capsids to study their self-assembly within an oscillatory environment. Thus far, our results have suggested a fundamental relationship between the orderly formation of capsids and the oscillation-enhanced ability of those capsids to correct errors that form during their growth. This result is in keeping with our general theoretical understanding of self-assembly, but extends it to these out-of-equilibrium conditions, where much biologically-relevant, as well as materials processing-related, assembly occurs. In related work, we are also working to simulate the folding of small, fast-folding lattice proteins within an oscillatory environment. This latter project was funded by the Jeffress Foundation. 

Figure 4: Environmental oscillations alter assembly. (a) Our 2D model of viral capsids are made up of attractive (green) and repulsive (blue) particles. (b) The efficiency of their assembly within an oscillatory environment depends not only upon the strength of the attractions between components, represented by the Lennard-Jones well-depth parameter, ε, but also upon the amplitude of oscillations in that parameter (the assembly in the non-oscillatory environment is shown in dark blue). (c) A lattice model of chignolin, a fast-folding peptide, whose folding we are currently studying under oscillatory conditions.

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