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Random walk in spherical coordinates 
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#1
Aug1010, 04:21 PM

P: 1

Hi,
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. 


#2
Aug1010, 08:40 PM

P: 1,261

Because the receptors are so much smaller than the size of the cell, it should be fine if you treat theta and phi just like xy; i.e. pretend its a 2D random walk in Cartesian coordinates.



#3
Aug1010, 11:08 PM

Sci Advisor
P: 6,109

To choose points on the surface of a sphere uniformly, the two angles should be chosen as follows (I'll call them latitude and longitude):
Longitude (θ)  θ uniform between 0 and 2π. Latitude (φ)  sinφ uniform between 1 and 1. 


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