Abstract
It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection–diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions. The interplay between advection and diffusion leads to behaviour that differs significantly from Brownian diffusion. We show that biologically plausible distributions of macromolecules can lead to highly non-Gaussian probability densities for the small particle position, including asymmetrical and multimodal densities. We confirm all our results using hard-sphere Brownian dynamics simulations.
Highlights
Cells are highly crowded environments, with up to 40% of the cytoplasmic volume occupied by macromolecules such as RNA, ribosomes and enzymes [1,2]
The motion of smaller molecules, such as amino acids and small proteins, is seriously impeded by macromolecular crowding: a large number of in vitro studies have shown that diffusion coefficients are reduced and binding rates increased in the presence of synthetic obstacles like dextran and Ficoll [2,3,4,5,6,7]
We address the question of how a purely steric heterogeneous crowder distribution affects the motion of a small particle
Summary
Cells are highly crowded environments, with up to 40% of the cytoplasmic volume occupied by macromolecules such as RNA, ribosomes and enzymes [1,2]. Phase separation is known to occur in the cytoplasm owing to hydrophobic and elecrostatic interactions between different macromolecular species, leading to distinct regions of high and low crowder density [24] These effects imply that the cell interior consists of a highly non-uniform distribution of crowders which is maintained over long time scales. Of behaviours observed in vivo [25,26], we show here that a steric description can explain a considerably wider variety of phenomena than usually thought, including multimodal densities, directed motion, and super- and subdiffusion This highly irregular behaviour is caused directly by the heterogeneity of the crowded environment, and so naturally would not be apparent in in vitro or computational studies which assume uniform crowder distributions.
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