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Hello,

I have some equations that describe the dynamics of a biological process. The equations are coupled bulk-membrane reaction diffusion equations. I have a system of PDE's, some of the PDE's have the bulk as the domain and some have the membrane. The variables on the membrane equations represent the concentration of some proteins on the membrane, these proteins are activated by receptors on the membrane. My end goal is to understand the protein dynamics caused by an initial pulse of receptors. I want to model the initial pulse of receptors almost as a gaussian pulse defined on the membrane. So for example, suppose that the membrane is represented as a sphere, then I would like to model the initial pulse of receptors as a gaussian function centered at a point of my choosing except that the function should actually be zero if one is far enough from the center of the pulse. Any comments or suggestion as to how I might achieve this? A more general question would be how do I define a function on a surface that varies only with space, not time, and can be used to define a nonlinear source term in a reaction-diffusion equation on said surface?

Many Thanks for your time.