Abstract
Biomolecular condensates in cells are often rich in catalytically active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathway. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically active particles. We show that a Michaelis–Menten-like dependence of the particles’ activities manifests itself as a screening of the interactions, and that a mixture of two differently sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.Graphic abstract
Highlights
In a recent publication [12], it was shown that the interplay between catalytic activity and chemotaxis can lead to effective non-reciprocal interactions [13,14,15] between enzyme-like particles, resulting in an active mechanism for the phase separation of such particles. This active phase separation is distinct from the non-equilibrium phase separation models that have been more coma e-mail: ramin.golestanian@ds.mpg.de monly put forward in the cell biological context [16], where the interactions between the different components are equilibrium ones, and the non-equilibrium aspect comes from fuelled chemical reactions that act as a source or sink of some of the phase-separating components
We will generalize the model studied in Ref. [12], by accounting for size polydispersity of the catalytically active particles involved in the mixture, as well as for the dependence of catalytic activity on the concentration of substrate
We show that under these conditions, the stability phase diagram of the particle mixture shows an extended instability region corresponding to a local instability, and can exhibit transient oscillations during a system-wide instability
Summary
We will generalize the model studied in Ref. [12], by accounting for size polydispersity of the catalytically active particles involved in the mixture, as well as for the dependence of catalytic activity on the concentration of substrate. We show that taking into account the dependence on substrate concentration leads to screening effects, which put a stricter activity threshold for the occurrence of a spatial instability. A model that simultaneously takes into account both of these effects is shown to exhibit a rich phase diagram, ranging from non- to partially to fully oscillatory. 3, we reveal a screening effect created by a dependence of the catalytic activity on the concentration of substrate, and conclude that this effect leads to an instability threshold and a local (as opposed to system-wide) instability. 5, we consider both screening and size dispersity effects combined, which leads to a complex stability phase diagram, which includes fully, partially, and non-oscillatory local instabilities
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