All living things are driven by chemical reactions. Reactions provide energy and transform matter. Thus, maintaining the system out of equilibrium. However, these chemical reactions have to be organized in space. One way for this spatial organization is via the process of phase separation. Motivated by the recent discovery of liquid-like droplets in cells, this thesis studies the organization of chemical reactions in phase-separated systems, with and without broken detailed balance. After introducing the underlying thermodynamic principles, we generalize mass-action kinetics to systems with homogeneous compartments formed by phase separation. Here, we discuss the constraints resulting from phase equilibrium on chemical reactions. We study the relaxation kinetics towards thermodynamic equilibrium and investigate non-equilibrium states that arise when detailed balance is broken in the rates of reactions such that phase and chemical equilibria contradict each other. We then turn to spatially continuous systems with spatial gradients within formed compartments. We derive thermodynamic consistent dynamical equations for reactions and diffusion processes in such systems. Again, we study the relaxation kinetics towards equilibrium and discuss non-equilibrium states. We investigate the dynamics of droplets in the presence of reactions with broken detailed balance. Furthermore, we introduce active droplet systems maintained away from equilibrium via coupling to reservoirs at their boundaries and organizing reactions solely within droplets. Here, detailed balance is only broken at the boundaries. Nevertheless, stationary chemically active droplets exist in open systems, and droplets can divide. To quantitatively study chemically active droplet systems in multi-component mixtures, we introduce an effective description. Therefore, we couple linearized reaction-diffusion equations via a moving interface within a sharp interface limit. At the interface, the boundary conditions are set by a local phase equilibrium and the continuity of fluxes. Equipped with these tools, we introduce and study protocell models of chemically active droplets. We explicitly model these protocells’ nutrient and waste dynamics, leading to simple models of their metabolism. Next, we study the energetics of these droplets and identify processes responsible for growth or shrinkage and maintaining the system out of equilibrium. Furthermore, we discuss the energy balance leading to the heating and cooling of droplets. Finally, we show why chemically active droplets do not spontaneously divide in two-dimensional systems with bulk-driven reactions. Here, droplets can elongate but do not pinch off. To have a minimal two-dimensional model with droplet division, we introduce additional reactions. When these reactions are localized at the interface and dependent on its mean curvature, droplets robustly divide in 2D. In summary, this thesis contributes to the theoretical understanding of how the existence of droplets changes the kinetics of reactions and, vice versa, how chemical reactions can alter droplet dynamics.:1 Introduction 1.1 Thermodynamics of phase separation 1.1.1 Phase equilibrium in the thermodynamic limit 1.1.2 Relaxation dynamics towards equilibrium 1.1.3 Local stability of homogeneous phases 1.2 Thermodynamics of chemical reactions in homogenous mixtures 1.2.1 Conserved densities and reaction extents 1.2.2 Equilibrium of chemical reactions 1.2.3 Mass-action kinetics towards equilibrium 1.3 Simultaneous equilibrium of chemical reactions and phase separation 1.4 Chemical reactions maintained away from equilibrium 1.5 Structure of this thesis 2 Chemical reactions in compartmentalized systems 2.1 Mass-action kinetics for compartments built by phase separation 2.1.1 Dynamical equations for densities and phase volumes 2.1.2 Relaxation kinetics in a simple example 2.2 Driven chemical reactions in compartmentalized systems 2.2.1 Non-equilibrium steady states at phase equilibrium 2.2.2 The tie line selecting manifold 2.3 Discussion 3 Dynamics of concentration fields in phase-separating systems with chemical reactions 3.1 Reaction-diffusion equations for phase-separating systems 3.2 Relaxation towards thermodynamic equilibrium in spatial systems 3.2.1 Relaxation kinetics and fast diffusion 3.2.2 Relaxation kinetics with spatial gradients 3.3 Driven chemical reactions in phase-separating systems 3.3.1 Driven chemical reaction and fast diffusion 3.3.2 Non-equilibrium steady states and spatial gradients 3.3.3 Droplets growth and ripening with driven chemical reactions 3.4 Boundary-driven chemically active droplets 3.4.1 Droplets in open systems 3.4.2 Non-equilibrium steady droplets and shape instabilities 3.5 Discussion 4 Chemically active droplets in the sharp interface limit 4.1 Droplet dynamics via reaction-diffusion equations coupled by a moving interface 4.2 Stationary interface positions in spherical symmetry 4.2.1 Interface conditions in closed systems 4.2.2 Interface conditions in open systems 4.3 Shape instabilities of spherical droplets 4.4 Discussion 5 Models of protocells and their metabolism as chemically active droplets 5.1 Breaking detailed balance in protocell models 5.1.1 Boundary-driven protocell models 5.1.2 Bulk-driven protocell models 5.2 Protocell dynamics 5.2.1 Steady states droplets 5.2.2 Shape stability of spherical symmetric droplets 5.3 Energetics of protocells 5.3.1 Mass conservation and droplet growth or shrinkage 5.3.2 Energy conservation and droplet heating or cooling 5.4 Discussion 6 The role of dimensionality on droplet division 6.1 Stability of chemically active droplets in 2D vs. 3D 6.1.1 Stationary droplets in 1D, 2D and 3D 6.1.2 Elongation instability 6.1.3 Pinch-off instability 6.2 Pinch-off in 2D via curvature-dependent chemical reactions 6.2.1 Determining the mean curvature of the droplet interface 6.2.2 Chemical reactions at the interface 6.3 Discussion 7 Conclusion and Outlook A Free energy considerations B Surface tension in multi-component mixtures C Figure details Bibliography

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This research is focused on the investigation of phase morphology and blend stability within ionomeric perfluorocyclobutane (PFCB)/poly(vinylidene difluoride) (PVDF) copolymer blend membranes. The morphologies of these unique materials, designed as proton exchange membranes (PEMs) for proton exchange membrane fuel cells (PEMFCs), have been examined not only in the as-cast/as-received state, but also as a function of exposure to various ex-situ aging environments. The morphological investigations used to probe the response of these ionomer blends have been designed to mimic the environment within a PEMFC and will therefore enhance our understanding of the implications of morphological changes which may occur during fuel cell operation. Thermal annealing of the membranes has been conducted to determine the materials' morphological response to various temperatures in the absence of hydration. The results of these thermal annealing studies have facilitated the isolation of morphological contributions stemming from thermal exposure. Immersion of the blend membranes in liquid water has allowed for singular identification of the role of hydration in the blend membranes' morphological rearrangement and phase stability. However, as the typical fuel cell environment to which these membranes will be exposed is complicated by the presence of both temperature and humidity, our ex-situ investigations have also included the exposure of PFCB/PVDF copolymer blend membranes to simultaneous thermal annealing and hydration conditions – a treatment we refer to as "hygrothermal aging." This unique procedure serves as a simplified method whereby the complex fuel cell environment may be simulated, and the resultant morphological response researched. While the work presented herein has enhanced our understanding of the blend stability of the specific membranes investigated, we have also advanced the fundamental knowledge of the role of morphology with respect to the fuel cell performance of blend materials and the corresponding implications of morphological rearrangements. Such an understanding is essential in the development of morphology-property relationships and eventual optimization of membrane materials designed for use in fuel cells. / Ph. D.

The primary objective of this research is to generate reinforcing domains in situ during the processing of polymers by using phase separation techniques. Low molecular weight compounds were mixed with polymers where the process viscosity is reduced at process temperatures and mechanical properties are improved once the material system is cooled or reacted. Thermally induced phase separation and thermotropic phase transformation of low molar mass compounds were used in isotactic polypropylene (iPP) and poly(ether ether ketone) (PEEK) resins. Reaction induced phase separation was utilized in thermosets to generate anisotropic reinforcements. A new strategy to increase fracture toughness of materials was introduced. Simultaneously, enhancement in stiffness and reduction in process viscosity were also attained. Materials with improved rheological and mechanical properties were prepared by using thermotropic phase transformations of metal soaps in polymers (calcium stearate/iPP). Morphology and thermal properties were studied using WAXS, DSC and SEM. Mechanical and rheological investigation showed significant reduction in process viscosity and substantial improvement in fracture toughness were attained. Effects of molecular architecture of metal soaps were investigated in PEEK (calcium stearate/PEEK and sodium stearate/PEEK). The selected compounds reduced the process viscosity due to the high temperature co-continuous morphology of metal soaps. Unlike the iPP system that incorporates spherical particles, interaction between PEEK and metal soaps resulted in two discrete and co-continuous phases of PEEK and the metal stearates. DMA and melt rheology exhibited that sodium stearate/PEEK composites are stiffer. Effective moduli of secondary metal stearate phase were calculated using different composite theories, which suggested bicontinuous morphology to the metal soaps in PEEK. Use of low molecular weight crystallizable solvents was investigated in reactive systems. Formation of anisotropic reinforcements was evaluated using dimethyl sulfone (DMS) as the crystallizable diluent and diglycidyl ether of bisphenol-A (DGEBA)/m-phenylene diamine (mPDA) material system as the epoxy thermoset. Miscible blends of DMS and DGEBA/mPDA form homogenous mixtures that undergo polymerization induced phase separation, once the DGEBA oligomers react with mPDA. The effect of the competition between the crystallization and phase separation of DMS resulted in nano-wires to micro-scale fiber-like crystals that were generated by adjusting the reaction temperature and DMS concentration.

Stem cells, with the ability to self-renew and differentiate into intended cell types, are a valuable tool for disease modeling and mechanistic study. CRISPR-Cas9 has been widely used for genome editing due to its high efficiency and convenience. However, CRISPR-Cas9 has large-deletion safety issues that dramatically restrict its applications. Wiskott-Aldrich syndrome (WAS) is an inborn immunological disorder caused by WASP deficiency. WASP functions in the nucleus, which may help to understand WAS pathology, are poorly defined. Pannexin 1 (PANX1) forms large plasma membrane pores to exchange intracellular small molecules with the extracellular environment and functions in inflammatory processes. The regulatory mechanisms of the PANX1 channel remain obscure. In this dissertation, I focused on mechanistic studies of CRISPR-Cas9 genome editing, and two immune disease relevant genes, WASP and PANX1 using stem cell-derived immune cells. We first found that CRISPR-induced large deletions (LDs) are predominantly mediated by the MMEJ repair pathway through statistical studies. Further, we found POLQ and RPA play vital roles in CRISPR-induced LDs. Modulation of POLQ and RPA can decrease CRISPR-induced LDs and increase HDR efficiency. Using three isogenic WAS iPSC models generated via gene editing, we successfully recapitulated WAS phenotypes, and for the first time, revealed that WASP regulates RNA splicing via epigenetically controlling the transcription of splicing factors and directly participating in the splicing machinery through a liquid-liquid phase separation process. We established a full-length human PANX1 (hPANX1) channel model via cryo-electron microscopy experiments and molecular dynamics simulation study, and found that hPANX1 channel is a homo-heptamer with both the N- and C-termini stretching deeply into the pore funnel. Functional studies of three selected residues support the new hPANX1 channel model and suggest the potential regulatory role of hPANX1 in pyroptosis upon immune responses. Overall, the mechanistic studies of WASP, PANX1 and CRISPR genome editing revealed new roles of WASP in regulating RNA splicing, new functional insights of PANX1 in pyroptosis, and uncovered two critical players POLQ and RPA in CRISPR-induced LDs.

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