Listeria, like all bacteria, emit small molecules as waste products or for signaling. Here we will consider a "race" between a Listeria bacterium (about 1 um across) and a chemical signal it emits while inside a much larger (~ 15 µm) mammalian cell. Suppose the Listeria bacterium, when at one end of the mammalian cell, emits a pulse of signaling molecules which begin diffusing through the mammalian cell. The Listeria then moves along a straight line from one end of the mammalian cell to the other. a. Write down the equation for the rms distance, assuming the diffusion is three-dimensional. Explain in words what the rms distance means (that is, what it tells us about a diffusion process).

Human Anatomy & Physiology (11th Edition)
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Chapter1: The Human Body: An Orientation
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Listeria, like all bacteria, emit small molecules as waste products or for
signaling. Here we will consider a "race" between a Listeria bacterium
Mammalian cell
(about 1 um across) and a chemical signal it emits while inside a much larger
(~ 15 um) mammalian cell. Suppose the Listeria bacterium, when at one
end of the mammalian cell, emits a pulse of signaling molecules which begin
diffusing through the mammalian cell. The Listeria then moves along a
straight line from one end of the mammalian cell to the other.
a. Write down the equation for the rms distance, assuming the
Listeria
diffusion is three-dimensional. Explain in words what the rms
distance means (that is, what it tells us about a diffusion process).
b. Using a diffusion constant of 200 um? /s, about how long does it take the signaling molecules to reach
the other side of the mammalian cell?
Transcribed Image Text:Listeria, like all bacteria, emit small molecules as waste products or for signaling. Here we will consider a "race" between a Listeria bacterium Mammalian cell (about 1 um across) and a chemical signal it emits while inside a much larger (~ 15 um) mammalian cell. Suppose the Listeria bacterium, when at one end of the mammalian cell, emits a pulse of signaling molecules which begin diffusing through the mammalian cell. The Listeria then moves along a straight line from one end of the mammalian cell to the other. a. Write down the equation for the rms distance, assuming the Listeria diffusion is three-dimensional. Explain in words what the rms distance means (that is, what it tells us about a diffusion process). b. Using a diffusion constant of 200 um? /s, about how long does it take the signaling molecules to reach the other side of the mammalian cell?
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