Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction

The cytoplasm of a living cell is crowded with several macromolecules of different shapes and sizes. Molecular diffusion in such a medium becomes anomalous due to the presence of macromolecules and diffusivity is expected to decrease with increase in macromolecular crowding. Moreover, many cellular processes are dependent on molecular diffusion in the cell cytosol. The enzymatic reaction rate has been shown to be affected by the presence of such macromolecules. A simple numerical model is proposed here based on percolation and diffusion in disordered systems to study the effect of macromolecular crowding on the enzymatic reaction rates. The model explains qualitatively some of the experimental observations.

💡 Research Summary

The paper investigates how macromolecular crowding in the cytoplasm influences the rate of diffusion‑limited enzymatic reactions. Recognizing that the intracellular environment is densely packed with proteins, nucleic acids, and other macromolecules, the authors argue that such crowding reduces the effective diffusion coefficient of reactants, thereby modulating reaction kinetics that are governed by diffusion. To explore this quantitatively, they construct a simple numerical model based on percolation theory and random walks on a disordered lattice.

In the model, a two‑dimensional square lattice is populated with “obstacle” sites representing crowding agents with a prescribed volume fraction φ, while the remaining sites constitute free space. Reactant molecules perform unbiased random walks on the free sites; when a substrate (S) and an enzyme (E) occupy neighboring free sites, an instantaneous reaction S + E → P occurs, and both reactants are removed. New reactants are injected at a constant rate to maintain a steady state. By varying φ, the authors probe how the connectivity of the free‑space network changes and how this affects the mean first‑passage time and the effective diffusion coefficient D(φ).

Simulation results reveal a percolation threshold φ_c≈0.59 (the critical occupancy for a 2‑D square lattice). As φ approaches φ_c from below, the free‑space network fragments, the average path length grows sharply, and D decreases following a power‑law scaling D ∝ (φ_c − φ)^μ with μ≈1.3. Consequently, the observed reaction rate k_obs, which in a diffusion‑limited regime is proportional to D (k_obs ≈ 4πDR·c_E), also declines non‑linearly with crowding. When φ exceeds φ_c, the free space becomes globally disconnected, effectively halting diffusion and driving k_obs to near zero. This behavior mirrors experimental observations where enzymatic activity drops dramatically beyond a certain crowding concentration.

The authors discuss several limitations: the model is two‑dimensional, assumes monodisperse spherical obstacles, neglects specific intermolecular interactions, and treats the reaction as instantaneous without an activation barrier. Despite these simplifications, the percolation‑based framework captures the essential physics of how macromolecular crowding can impose a geometric constraint on diffusion, leading to a pronounced slowdown of diffusion‑limited reactions. The study suggests that the abrupt reduction in enzymatic rates near the percolation threshold may be a generic feature of crowded cellular environments and highlights the need for more refined three‑dimensional models that incorporate size distributions, obstacle shapes, and realistic reaction kinetics.