Lecture 2 Bacteria Plasma Membrane Diffusion

Lecture 2 Bacteria Plasma Membrane Diffusion - BME 418...

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BME 418, Quantitative Cell Biology Alan J. Hunt 2 - Cell membrane, bacteria Cell membranes are lipid bilayers. This is how a cell maintains its internal environment: that is keeps what’s in, in and what's out, out. This can be an exceedingly difficult problem: for example, vacuums, hoses, roofs. Bilayers are an elegant solution since they are: 1) flexible, 2) easy to expand or contract, 3) self-sealing. But how well does this prevent exit and entry of chemicals and small molecules? Considering how thin and fluid a membrane is, we might expect that some molecules could cross. But which molecules, and how fast? To consider this we need to the bulk implications of diffusion. Diffusion in one dimension Start with a particle at position, x = 0, at time, t = 0, and battered about by random collisions with other particles. For simplicity assume δ is a constant increment of movement that occurs in a time interval τ . The probability of a step in the negative direction is the same as in the positive: P(- δ ) = P(+ δ ) = ½ And the expected mean position after n steps ( t = n τ ) is: 0 ) ( = n x What about the absolute displacement, that is: 2 1 2 ) ( n x ( 29 2 2 2 2 ) 1 ( 2 ) 1 ( ) 1 ( ) ( δ δ δ + - ± - = ± - = n x n x n x n x Now this can have many outcomes depending on the value of first and second terms. We can compute the average over these possible outcomes as:
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