Biophysics Equation for Cell Permeability: Alcohol Concentration Model

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SUMMARY

The discussion centers on the derivation of the equation governing alcohol concentration in a cell modeled as a spherical bag with a membrane permeability of P=20μms-1. The governing equation is -d(Δc)/dt = (3P/r)Δc, where Δc represents the concentration difference across the membrane. Participants suggest using Fick's laws of diffusion as a foundational concept for solving the equation. The conversation emphasizes the importance of integrating both sides after rearranging the equation to facilitate the solution.

PREREQUISITES
  • Understanding of Fick's laws of diffusion
  • Basic knowledge of differential equations
  • Familiarity with membrane permeability concepts
  • Concept of concentration gradients in biological systems
NEXT STEPS
  • Study Fick's laws of diffusion in detail
  • Learn about solving first-order differential equations
  • Research membrane permeability and its biological implications
  • Explore mathematical modeling of cellular processes
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Students in biophysics, researchers in cellular biology, and educators teaching concepts related to membrane dynamics and diffusion processes.

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Homework Statement


Consider a simple, physical model of a cell in which the cell is regarded as a spherical bag with radius r, bounded by a membrane permeable to alcohol with permeability, P=20μms-1. Show the concentration of alcohol in the cell is governed by this equation.

Homework Equations


-d(Δc)/dt = (3P/r)Δc

The Attempt at a Solution


I don't really know what to do with this, I don't really know where to start. The second bit of the question asks to solve the equation which I guess you can do by bringing dt over to the other side and dividing by Δc and integrating both sides, but I have no idea how to get the equation really.
 
Physics news on Phys.org
Have you learned any equations to find the flux of molecules across a membrane? Or, have you learned Fick's laws of diffusion? Either one could serve as a starting point for the derivation. (If not, here's a website with some explanations)
 

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