# Difference between revisions of "Intracellular transport by active diffusion"

Entry: Chia Wei Hsu, AP 225, Fall 2010

Clifford P. Brangwynne, Gijsje H. Koenderink, Frederick C. MacKintosh and David A. Weitz, "Intracellular transport by active diffusion" , Trends in Cell Biology 19 (9), 423-427 (2009).

## Summary

This article concerns cell mechanics. The main point of this article is that active transports in cells can result in significant random fluctuations of particles that resemble thermal fluctuations. These particles undergo an enhanced diffusion, which the authors refer to as "active diffusion".

## Background: Thermal diffusion and random intracellular motion

Thermal agitation causes molecules or small particles to perform random walk in a solution. This is referred to as Brownian motion or diffusive motion. Although diffusion is not directional, it acts as an important mechanism for short-distanced transports in cells and provides the basis for signal transduction networks.

Thermal-driven diffusion follows well-known physical laws. The diffusion constant increases with temperature, and decreases with the particle size and the medium viscosity. However, a number of intracellular motions appear to be random and diffusive-like, but do not follow these basic properties of thermal diffusion. This suggests that there must be other mechanism that contributes to the random transport of particles in cells.

In cells, there is another kind of transport. These are active, directional transports driven by either the motion of motor proteins along cytoskeletal filaments (kinesins and dyneins run on microtubules; myosins run on actin), or the polymerization/de-polymerization of these filaments. These directed transports are distinct from the random diffusive transport.

This article discusses how the active transports can drive random diffusive-like transports.

## Coupling between mechanics and diffusivity

Fig. 1. Schematic plots for active and thermal fluctuation motion of an inert probe particle in cell.

The authors discuss how diffusivity is connected to the mechanics, by the example of actin networks. At low actin concentrations, the solution behaves as a viscous liquid, and the mean-square-displacement (MSD) of the filaments grows linearly with time. At high actin concentration, filaments cross-link and behaves like an elastic solid, and MSD remains at a small fixed value. At intermediate actin concentrations, the filaments behaves as a viscoelastic material and undergo sub-diffusive motion with MSD increases with time but slower than linear.

## Thermal diffusion vs active diffusion

Without other activities in cells, an inert probe particle is expected to undergo sub-diffusive motion on short time scales (t ~ 1 sec), hindered motion for longer time scales (t ~ 10 sec), and diffusive motion on even-longer time scales (t > 100 sec). This expected curve is described by the blue line in fig 1.

With active motions in cells, the motion of an inert probe particle is actually better described by the red line in fig 1. For example, the myosin motors can "fluidize" the actin network by enhancing the ability of filaments to slide past one another. Thus the probe particles are less hindered, and undergoes diffusive-like motion at short time scales. At long time scales, the motors actively remodels the filament network, which also enhances the mobility of the probe particle. These observations are supported by both in vitro and in situ experiments.

## Connection to soft matter

In soft matter, we frequently treat thermal fluctuations as the source of diffusion, and use the Stokes-Einstein relation $D=k_B T / 6 \pi \eta R$ to estimate the diffusion constant of a particle with Stokes radius $R$ in a medium with viscosity $\eta$. However, this article tells us that such approach will be fundamentally incorrect when we look at the motion of particles in cell, where active transport motions are constantly going on. The motion of such particles are random on average, but can no longer be described by simple physical laws. This is another reason why it is so hard to quantify cell mechanics.