[Paper Review] Catalysis-Induced Phase Separation and Autoregulation of Enzymatic Activity

Matthew W. Cotton, Ramin Golestanian+1 more|arXiv (Cornell University)|May 24, 2022

Protein Structure and Dynamics48 references23 citations

TL;DR

This paper proposes a novel mechanism—catalysis-induced phase separation (CIPS)—where enzymatic activity alone drives phase separation in enzyme-substrate-product mixtures without equilibrium interactions. By generating chemical gradients that induce effective enzyme-enzyme attraction via phoretic mobility differences, CIPS leads to spontaneous condensation and autoregulates enzymatic activity through feedback, offering a non-equilibrium basis for biological organization.

ABSTRACT

We present a thermodynamically consistent model describing the dynamics of a multi-component mixture where one enzyme component catalyzes a reaction between other components. We find that the catalytic activity alone can induce phase separation for sufficiently active systems and large enzymes, without any equilibrium interactions between components. In the limit of fast reaction rates, binodal lines can be calculated using a mapping to an effective free energy. We also explain how this catalysis-induced phase separation (CIPS) can act to autoregulate the enzymatic activity, which points at the biological relevance of this phenomenon.

Motivation & Objective

• To investigate whether enzymatic activity alone can induce phase separation without equilibrium interactions.
• To explain how catalytic activity generates effective interactions via chemical gradients and phoresis.
• To establish a thermodynamically consistent framework linking non-equilibrium catalysis to phase behavior.
• To demonstrate that CIPS naturally leads to autoregulation of enzymatic activity.
• To connect the model to existing theories of phase separation and non-equilibrium thermodynamics.

Proposed method

• Uses non-equilibrium thermodynamics and Flory-Huggins theory to model a multi-component fluid with conserved component volume fractions.
• Introduces a catalyzed reaction E + S + F ⇌ E + P + W with a fuel reservoir maintaining constant µF and µW.
• Models transport via Onsager reciprocal relations and mobility matrices Mij = −βDijφiφj, with Dij representing cross-diffusion coefficients.
• Derives effective interactions through phoretic mobility differences (Dpe > Dse), leading to enzyme accumulation in regions of substrate depletion or product enrichment.
• Maps the non-equilibrium system to an effective free energy to calculate binodal and spinodal lines, enabling equilibrium-like phase diagram analysis.
• Applies the Maxwell-Stefan formalism as an equivalent framework to describe multicomponent diffusion and link to measurable transport coefficients.

Experimental results

Research questions

• RQ1 Can enzymatic activity alone induce phase separation without equilibrium interactions between components?
• RQ2 How do chemical gradients generated by catalysis lead to effective enzyme-enzyme attraction?
• RQ3 What is the role of differential phoretic mobilities (Dpe vs. Dse) in driving phase separation?
• RQ4 Can the non-equilibrium system be mapped to an effective free energy to predict binodal and spinodal lines?
• RQ5 How does CIPS lead to autoregulation of enzymatic activity through feedback?

Key findings

• Catalysis-induced phase separation (CIPS) occurs when Dpe > Dse, leading to effective enzyme-enzyme attraction and spontaneous phase separation without equilibrium interactions.
• Phase separation is driven by non-equilibrium chemical gradients, with enzymes accumulating in regions of low substrate or high product concentration.
• The system can be mapped to an effective free energy, allowing calculation of binodal and spinodal lines, with a critical point where they meet.
• CIPS leads to a reduction in overall catalytic activity, demonstrating intrinsic autoregulation of enzymatic function.
• The model predicts that enzyme diffusion in response to substrate and product gradients (phoretic mobility) determines instability, with µes − µep > 0 required for CIPS.
• Experimental measurements of enzyme diffusion and phoretic mobility in water can be used to extract Dse and Dpe, validating the model’s predictive power.