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I'm modeling receptors moving along a cell surface that interact with proteins inside of a cell. I figured it would be easier to model the receptors in spherical coordinates, however I'm unsure of how to model a random walk. In cartesian coordinates, I basically model a step as:

x = x + sqrt(6*D*timeStep)*randn

y = y + sqrt(6*D*timeStep)*randn

z = z + sqrt(6*D*timeStep)*randn

Where D is my diffusion constant. How can I do this just using theta and phi? Modeling random walk in spherical coordinates will be really nice, because I can fix r such that the receptors can't leave the membrane of the cell, and just focus on how it moves in 2D with respect to the membrane.

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# Random walk in spherical coordinates

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