Chemical reactions controlled through compartmentalization: Applications to bottom-up design of synthetic life

Liquid-liquid phase separation (LLPS) has been proposed as the underlying physical principle leading to the formation of membrane-less organelles in eukaryotic cells, following advancements, in the last two decades, in experimental observations owing to progress in confocal microscopy. These organelles can act as compartments in sequestering molecules and tuning rates of biochemical reactions, among a repertoire of functions they serve. Biochemical reactions are constantly in progress in living cells and are driven out of equilibrium due to fuel consumption in the form of ATP or GTP molecules. Free diffusion of reactive molecules through these compartments leads to their spatiotemporal sequestration and automatically implies an interplay between phase separation and chemical reactions. In this work, we are specifically interested to understand how the two processes closely affect each other and applying the understanding to tune better bottom-up design principles for synthetic life, which involves coupling compartmentalization and chemical reactions. The first part of this work is devoted to studying the interplay between phase separation and chemical reactions. To this end, we developed the theory of mass action kinetics of equilibrium and out-of-equilibrium processes occurring at phase equilibrium in a multicomponent mixture. Phase equilibrium is imposed at all times, thus restricting the chemical kinetics to the binodal manifold. We learn more about circumstances in which reaction rates can differ in coexisting phases. Next, we decouple the phase-forming components (scaffolds) and the dilute reactive components (clients), which means that the reactive dilute components respond to the heterogeneous profile in the system set by the scaffold but do not affect it. This allows us to investigate to what extent compartments can affect chemical reactions in terms of their yield at steady state for a bimolecular reaction or initial reaction rate for a nucleation process compared to the absence of compartments. We use the effective droplet model and mass reaction kinetics at phase equilibrium to address the above questions. We can understand better how the properties of reactions can be optimally tuned by compartment size. Following the theoretical developments in the first part of this work, we proceed to use the theoretical model of mass action kinetics at phase equilibrium to study emergent properties of parasitic behavior in a system composed of multiple fuel-driven reaction cycles, which lead to the formation of so-called 'building blocks' which can phase separate. This study also helps us probe the buffering capacity of phase separation. It further provides insights into how the lifetime of reactive 'building blocks' can be tuned via phase separation. Synthetic cells are generally realized by localizing minimalistic reactions in micron-scale water-filled environments, thus mimicking compartmentalization. Here we apply our model to understand how the localization of an autocatalytic process (PEN-DNA reaction) inside proteinosomes affect the reaction rates compared to the reactions in a homogeneous buffer solution. To summarize, we developed theoretical approaches to study the interplay of chemical reactions with compartmentalization and apply such approaches to systems chemistry and synthetic biology experimental studies to unravel how reactions can be controlled through compartmentalization.:1 Introduction 1 1.1 Phase Separation - A brief overview of the development of the field . . . . . . 1 1.2 Thermodynamics of phase separation in a multi-component mixture . . . . . 4 1.2.1 Mean field free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Other possible free energy considerations: Beyond mean-field . . . . . 7 1.2.3 Exchange chemical potential, chemical activity and osmotic pressure . 8 1.2.4 Thermodynamic instability leads to phase separation . . . . . . . . . 9 1.2.5 Phase equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.6 Relaxation dynamics to phase equilibrium . . . . . . . . . . . . . . . . 13 1.3 Thermodynamics of chemical reactions in homogeneous mixtures . . . . . . . 14 1.3.1 Chemical equilibrium conditions . . . . . . . . . . . . . . . . . . . . . 14 1.3.2 Relaxation to chemical equilibrium . . . . . . . . . . . . . . . . . . . . 16 1.4 Thermodynamic equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5 Scope of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Chemical reaction kinetics at phase equilibrium 21 2.1 Kinetics of chemical reactions relaxing to thermodynamic equilibrium . . . . 21 2.1.1 Volume fraction field and phase volume kinetics . . . . . . . . . . . . 22 2.1.2 Diffusive exchange rates between phases . . . . . . . . . . . . . . . . . 22 2.1.3 Reaction rates at phase equilibrium . . . . . . . . . . . . . . . . . . . 23 2.1.4 Properties of chemical reactions at phase equilibrium . . . . . . . . . 24 2.2 Unimolecular chemical reactions in coexisting phases . . . . . . . . . . . . . . 25 2.3 Bimolecular chemical reactions in coexisting phases . . . . . . . . . . . . . . . 27 2.4 Chemical reactions maintained away from chemical equilibrium . . . . . . . . 28 2.4.1 Tie-line selecting curve . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3 Chemical reactions of dilute clients in phase-separated compartments 33 3.1 Thermodynamics of a multicomponent mixture of scaffold and clients . . . . 34 3.1.1 Phase equilibrium conditions: Dilute client limit . . . . . . . . . . . . 35 3.1.2 Relaxation dynamics to phase equilibrium: Dilute client limit . . . . . 38 3.1.3 Chemical equilibrium conditions: Dilute client limit . . . . . . . . . . 40 3.1.4 Relaxation dynamics to chemical equilibrium: Dilute client limit . . . 41 3.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Two-state transitions controlled by a drop . . . . . . . . . . . . . . . . 43 3.2.2 Bimolecular reaction controlled by a drop . . . . . . . . . . . . . . . . 45 3.2.3 Nucleation reaction controlled by a drop . . . . . . . . . . . . . . . . . 47 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4 Fuel-driven chemical reactions in the dilute phase at phase equilibrium 50 4.1 Chemical reaction network and its properties . . . . . . . . . . . . . . . . . . 51 4.1.1 Observations from individual reaction cycles . . . . . . . . . . . . . . 52 4.1.2 Observations from combined reaction cycles . . . . . . . . . . . . . . . 53 4.2 Kinetic equations at phase equilibrium . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Construction of the ternary phase diagram . . . . . . . . . . . . . . . . . . . . 57 4.4 Mechanism of co-phase separation . . . . . . . . . . . . . . . . . . . . . . . . 58 4.4.1 Composition of droplets . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.5 Co-phase separation with periodic fueling . . . . . . . . . . . . . . . . . . . . 61 4.6 Effects of activation rate constants on host-parasite identity . . . . . . . . . . 63 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5 Study of enzymatic kinetics in compartmentalized systems 65 5.1 Autocatalytic reactions and their properties . . . . . . . . . . . . . . . . . . . 66 5.2 PEN DNA mass action kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.3 Proteinosomes affect the PEN DNA reactions . . . . . . . . . . . . . . . . . . 70 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6 Conclusion and Outlook 72 A Free energy calculations for block charged polymers using RPA 76 B Numerical Methods 79 C Linear first order corrections to scaffold equilibrium volume fractions 83 D Dynamic equations in dilute limit 86 E Spatial solutions 88 F Fitting routine and extracted rate coefficients 90 G Experimental methods 95 H Calibration constants and reaction rate coefficients of PEN DNA study 98 List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10