Macromolecular crowding directs the motion of small molecules inside cells

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.

Accurate and efficient discretisations for stochastic models providing near agent-based spatial resolution at low computational cost

“…Since crowding eects are important in cell biology assays [5,7,9,16,25], the CBM is an exclusion process, as both movement and proliferation processes may only take place if the target compartment (i.e., either the same or an adjacent compartment of the agent undergoing these processes), has sucient space to accommodate potential motility and movement events. For lattice-based models, such as the CBM, the excluded volume is the volume occupied by agents; however, this equivalence is not true for lattice-free agent-based models [35,36]. At any time, a randomly chosen isolated agent has a transition rate r m per unit time of moving (either within the same compartment or to an adjacent compartment), a proliferation rate r p per unit time of giving rise to another agent (placed either in the same or an adjacent compartment), and a death rate r d per unit time (agent is removed).…”

Molecular simulations of cellular processes

“…Another limitation is that particle-based simulations have not been designed to probe non-uniform configurations arising, for example, from the cellular co-localization of macromolecules. Toward this aim, Smith et al (2017) combined theory and Brownian simulations to demonstrate that, in a non-uniform distribution of inert crowders, a particle may experience a transient super-diffusion upon transitioning from a dense to a less dense region of the cytoplasm. Their simulations showed that the biologically relevant scenario of nonuniform macromolecular distribution might induce super-diffusion, therefore directing macromolecule motion even in the absence of active transport.…”

“…An additional consequence of the high concentration of macromolecules in vivo is that mobility can be anomalous, i.e., the diffusion coefficients can be time-dependent, contrary to the constant values expected in isolation (Banks and Fradin 2005;Dix and Verkman 2008;Smith et al 2017). A positive rate of diffusion, termed super-diffusion, often suggests a mechanism of active transport (Reverey et al 2015).…”

Spatial moment description of birth-death-movement processes incorporating the effects of crowding and obstacles

“…ECM geometry and microarchitecture play a significant role in regulating the motility of cancer (Condeelis and Segall 2003) and immune cells (Bajenoff et al 2006). The highly compartmentalised structure of the cytoplasm and the presence of macromolecular obstacles such as nucleic acids, proteins and polysaccharides in intracellular environments is known to have a significant impact on both biochemical reactions (Minton 2001;Tan et al 2013; Hansen et al 2016) and physical transport processes inside the cell ; Smith et al 2017). These examples from various organizational levels suggest that the incorporation of both obstacles and their crowding effects in a mathematical model of cell migration is important.…”

“…Some of these models consider the dynamics and interaction within a single population (Lewis 2000; Middleton et al 2014). Other models, often called multi-species models, directly incorporate the influence of interaction among different types of agents to represent different subpopulations (Murrell 2005; Plank and Law 2015; Smith et al 2017).…”