| dc.description.abstracteng | Biological cells need to structure their interior in space and time. One way this is done are
containers enclosed by a membrane as a physical barrier that can control which molecules enter
and leave the container. Another, recently discovered, class are biomolecular condensates.
These are liquid like droplets that form via liquid liquid phase separation. Although they have
no membrane, they do have distinctly different composition from the surrounding. Weak attractive
interactions between the molecules in the condensate prevent them from diffusing out
of the condensate. To control the formation and dissolution of these condensates, the cell can
change the attractive interaction between molecules via chemical reactions.
In this thesis, we develop a theory of phase separation with chemical reactions based on
thermodynamic arguments. The chemical reactions switch between two states of a protein, one
state phase separates and forms droplets, while the other state is soluble in the solvent. The
aim of this thesis was to analyze how such simple reactions can control the phase separation
process, for example, the formation, dissolution, and size control of droplets.
In the first part of the thesis, we investigate equilibrium reactions. In this case, the system
relaxes to thermodynamic equilibrium. Unlike two component fluids, fluids consisting of
multiple components with equilibrium reactions can form droplets, depending on the system
parameters. We find that equilibrium reactions introduce a new parameter to control phase
separation, the internal energy difference between the two protein states. This internal energy
difference can control how much protein is in the phase separating state and thereby, if droplets
form or not. We show that the droplet size is very sensitive to changes in the internal energy
difference. However, the parameter range for control of droplets is narrow. In addition, the
internal energy difference is an equilibrium property of the proteins, thus, it can not be changed
fast or in a specific manner.
In the second part of the thesis, we extend our model to non-equilibrium reactions. In this
case, the reaction is coupled to fuel molecules, which introduce external energy into the system
and drive the reaction away from thermodynamic equilibrium. The external driving strength is
a new parameter, which describes how strong the system is driven from equilibrium. We find,
that driven reactions alone can be mapped onto an effective equilibrium system with rescaled
internal energy difference that depends on the driving strength. This is different if both reaction
pathways, the driven and equilibrium reaction, are present. In this case, the total amount
of phase separating proteins depends on the reaction kinetics, i.e. on the relative reaction rates
of the two pathways. We show that this allows precise, fast and specific control over droplet
formation and dissolution. The reason is, that the kinetic parameters can be tuned by enzymes
that act only on specific reactions. Finally, motivated by experimental observations, we investigate
what happens if enzymes that catalyze the driven reaction are enriched in the droplet
phase. We find that the enzymatic enrichment can control individual droplet size and stabilize
multiple droplets of the same size against their thermodynamic tendency to form one big
droplet.
We show that size control of droplets by reactions is based on three specific features of
the reactions. (i) A protein exists in a soluble and a phase separating state and the transition
between the two states can be described as a chemical reaction. (ii) There are at least two
reaction pathways for the transition and at least one has to be driven out of equilibrium. (iii) The
reaction rates in droplet and solvent phase need to be different, for example, due to enrichment
of enzymes in the droplet.
More generally, our results highlight that chemical reactions in phase separating environments
can not be described by standard mass action kinetics. The reason is that phase separating
systems are inherently non-ideal and mass action kinetics are only valid in ideal, dilute
solutions. Instead, a thermodynamic treatment of reactions is necessary, which takes into account
that droplets formed by phase separation are chemically different from the solvent phase
due to enthalpic interactions. | de |