Question #21: How far would a typical molecule diffuse in a millisecond?

What is diffusion?

Diffusion is a type of passive transport that involves the net movement of molecules or ions from an area of higher concentration to an area of lower concentration down a concentration gradient. The concentration gradient is the difference in concentration between two points.

In biology, diffusion plays an important role in many biological events such as molecular transport, cell signaling, and neurotransmitter movement across a synaptic cleft.

How far would a typical molecule diffuse in a millisecond? A second? An hour?

Diffusion is a description of how molecules will randomly move around in a liquid. Their movement will be limited if they hit a barrier or randomly collide with another molecule and react, which is not described by diffusion.

The distance a molecule will diffuse in a certain amount of time depends on the size of the molecule, the viscosity of the fluid, and the temperature.

This can be explained by the Stokes-Einstein relation: D = kT/(6πηa), where:

– D = the diffusion constant

– k = the Boltzmann constant

– T = the temperature

– η = the viscosity coefficient of the fluid

– a = the radius of the diffusing molecule

The constant value is 6 assuming that the radius of the diffusing molecule is greater than the radius of the solvent.

Assuming that we are talking about diffusion at 25° C and in water, then there is a nice calculator on physiologyweb.com that lists diffusion coefficients for different ions and molecules:

https://www.physiologyweb.com/calculators/diffusion_time_calculator.html

If we are talking about the diffusion of a small molecule neurotransmitter such as glutamate, it has a MW of 147, which is close to glucose’s MW of 180. So we can use glucose’s diffusion coefficient as a rough guide for the diffusion of some types of small molecule neurotransmitters.

This calculator suggests that glucose will diffuse 1000 nm in a millisecond, 31,000 nm (31 μm) in a second, or 1,900,000 nm (1.9 mm) in an hour.

Molecular diffusion rates are helpful when building intuition about what structural information is necessary to be able to infer in brain preservation. Because, in the way that I think about it, molecular events that occur more slowly than rapid long-term memory recall can be instantiated (which, conservatively, can occur in ~500-1000 ms) cannot be uniquely necessary for the structural information describing it.

Inspired by CalTech’s Question #21 for cognitive scientists: “What is diffusion? How far would a typical molecule diffuse in a millisecond? A second? An hour? How does the diffusion equation differ from the cable equation?”