Mechanochemistry for Active Materials and Devices

The coupling of mechanical stress fields in polymers to covalent chemistry (polymer mechanochemistry) has provided access to previously unattainable chemical reactions and polymer transformations. In the bulk, mechanochemical activation has been used as the basis for new classes of stress-responsive polymers that demonstrate stress/strain sensing, shear-induced intermolecular reactivity for molecular level remodeling and self-strengthening, and the release of acids and other small molecules that are potentially capable of triggering further chemical response. The potential utility of polymer mechanochemistry in functional materials is limited, however, by the fact that to date, all reported covalent activation in the bulk occurs in concert with plastic yield and deformation, so that the structure of the activated object is vastly different from its nascent form. Mechanochemically activated materials have thus been limited to “single use” demonstrations, rather than as multi-functional materials for structural and/or device applications. Here, we report that filled polydimethylsiloxane (PDMS) elastomers provide a robust elastic substrate into which mechanophores can be embedded and activated under conditions from which the sample regains its original shape and properties. Fabrication is straightforward and easily accessible, providing access for the first time to objects and devices that either release or reversibly activate chemical functionality over hundreds of loading cycles.

While the mechanically accelerated ring-opening reaction of spiropyran to merocyanine and associated color change provides a useful method by which to image the molecular scale stress/strain distribution within a polymer, the magnitude of the forces necessary for activation had yet to be quantified. Here, we report single molecule force spectroscopy studies of two spiropyran isomers. Ring opening on the timescale of tens of milliseconds is found to require forces of ~240 pN, well below that of previously characterized covalent mechanophores. The lower threshold force is a combination of a low force-free activation energy and the fact that the change in rate with force (activation length) of each isomer is greater than that inferred in other systems. Importantly, quantifying the magnitude of forces required to activate individual spiropyran-based force-probes enables the probe behave as a “scout” of molecular forces in materials; the observed behavior of which can be extrapolated to predict the reactivity of potential mechanophores within a given material and deformation.

We subsequently translated the design platform to existing dynamic soft technologies to fabricate the first mechanochemically responsive devices; first, by remotely inducing dielectric patterning of an elastic substrate to produce assorted fluorescent patterns in concert with topological changes; and second, by adopting a soft robotic platform to produce a color change from the strains inherent to pneumatically actuated robotic motion. Shown herein, covalent polymer mechanochemistry provides a viable mechanism to convert the same mechanical potential energy used for actuation into value-added, constructive covalent chemical responses. The color change associated with actuation suggests opportunities for not only new color changing or camouflaging strategies, but also the possibility for simultaneous activation of latent chemistry (e.g., release of small molecules, change in mechanical properties, activation of catalysts, etc.) in soft robots. In addition, mechanochromic stress mapping in a functional actuating device might provide a useful design and optimization tool, revealing spatial and temporal force evolution within the actuator in a way that might also be coupled to feedback loops that allow autonomous, self-regulation of activity.

In the future, both the specific material and the general approach should be useful in enriching the responsive functionality of soft elastomeric materials and devices. We anticipate the development of new mechanophores that, like the materials, are reversibly and repeatedly activated, expanding the capabilities of soft, active devices and further permitting dynamic control over chemical reactivity that is otherwise inaccessible, each in response to a single remote signal.

Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Comparison of dynamic balance in adolescent male soccer players from rwanda and the United States.

PURPOSE/BACKGROUND: Dynamic balance is an important component of motor skill development. Poor dynamic balance has previously been associated with sport related injury. However, the vast majority of dynamic balance studies as they relate to sport injury have occurred in developed North American or European countries. Thus, the purpose of this study was to compare dynamic balance in adolescent male soccer players from Rwanda to a matched group from the United States. METHODS: Twenty-six adolescent male soccer players from Rwanda and 26 age- and gender-matched control subjects from the United States were screened using the Lower Quarter Y Balance Test during their pre-participation physical. Reach asymmetry (cm) between limbs was examined for all reach directions. In addition, reach distance in each direction (normalized to limb length, %LL) and the composite reach score (also normalized to %LL) were examined. Dependent samples t-tests were performed with significant differences identified at p<0.05. RESULTS: Twenty-six male soccer players from Rwanda (R) were matched to twenty-six male soccer players from the United States (US). The Rwandan soccer players performed better in the anterior (R: 83.9 ± 3.2 %LL; US: 76.5 ± 6.6 %LL, p<0.01), posterolateral (R: 114.4 ± 8.3 %LL ; US: 106.5 ± 8.2 %LL, p<0.01) and composite (R: 105.6 ± 1.3 %LL; US: 97.8 ± 6.2 %LL, p<0.01) reach scores. No significant differences between groups were observed for reach asymmetry. CONCLUSIONS: Adolescent soccer players from Rwanda exhibit superior performance on a standardized dynamic balance test as comparison to similar athletes from the United States. The examination of movement abilities of athletes from countries of various origins may allow for a greater understanding of the range of true normative values for dynamic balance. LEVELS OF EVIDENCE: 3b.

Evolution of networks and sequences in eukaryotic cell cycle control.

The molecular networks regulating the G1-S transition in budding yeast and mammals are strikingly similar in network structure. However, many of the individual proteins performing similar network roles appear to have unrelated amino acid sequences, suggesting either extremely rapid sequence evolution, or true polyphyly of proteins carrying out identical network roles. A yeast/mammal comparison suggests that network topology, and its associated dynamic properties, rather than regulatory proteins themselves may be the most important elements conserved through evolution. However, recent deep phylogenetic studies show that fungal and animal lineages are relatively closely related in the opisthokont branch of eukaryotes. The presence in plants of cell cycle regulators such as Rb, E2F and cyclins A and D, that appear lost in yeast, suggests cell cycle control in the last common ancestor of the eukaryotes was implemented with this set of regulatory proteins. Forward genetics in non-opisthokonts, such as plants or their green algal relatives, will provide direct information on cell cycle control in these organisms, and may elucidate the potentially more complex cell cycle control network of the last common eukaryotic ancestor.

Different Mechanisms Confer Gradual Control and Memory at Nutrient- and Stress-Regulated Genes in Yeast.

Cells respond to environmental stimuli by fine-tuned regulation of gene expression. Here we investigated the dose-dependent modulation of gene expression at high temporal resolution in response to nutrient and stress signals in yeast. The GAL1 activity in cell populations is modulated in a well-defined range of galactose concentrations, correlating with a dynamic change of histone remodeling and RNA polymerase II (RNAPII) association. This behavior is the result of a heterogeneous induction delay caused by decreasing inducer concentrations across the population. Chromatin remodeling appears to be the basis for the dynamic GAL1 expression, because mutants with impaired histone dynamics show severely truncated dose-response profiles. In contrast, the GRE2 promoter operates like a rapid off/on switch in response to increasing osmotic stress, with almost constant expression rates and exclusively temporal regulation of histone remodeling and RNAPII occupancy. The Gal3 inducer and the Hog1 mitogen-activated protein (MAP) kinase seem to determine the different dose-response strategies at the two promoters. Accordingly, GAL1 becomes highly sensitive and dose independent if previously stimulated because of residual Gal3 levels, whereas GRE2 expression diminishes upon repeated stimulation due to acquired stress resistance. Our analysis reveals important differences in the way dynamic signals create dose-sensitive gene expression outputs.

RNA Virus Evolution: a Cross-scale, Disease Dynamic Perspective

RNA viruses are an important cause of global morbidity and mortality. The rapid evolutionary rates of RNA virus pathogens, caused by high replication rates and error-prone polymerases, can make the pathogens difficult to control. RNA viruses can undergo immune escape within their hosts and develop resistance to the treatment and vaccines we design to fight them. Understanding the spread and evolution of RNA pathogens is essential for reducing human suffering. In this dissertation, I make use of the rapid evolutionary rate of viral pathogens to answer several questions about how RNA viruses spread and evolve. To address each of the questions, I link mathematical techniques for modeling viral population dynamics with phylogenetic and coalescent techniques for analyzing and modeling viral genetic sequences and evolution. The first project uses multi-scale mechanistic modeling to show that decreases in viral substitution rates over the course of an acute infection, combined with the timing of infectious hosts transmitting new infections to susceptible individuals, can account for discrepancies in viral substitution rates in different host populations. The second project combines coalescent models with within-host mathematical models to identify driving evolutionary forces in chronic hepatitis C virus infection. The third project compares the effects of intrinsic and extrinsic viral transmission rate variation on viral phylogenies.