Cell Eng Molecular Dynamics

Stokes einstein equation

D=kbT/6pimuR

numerator: thermal energy
denominator: resistance to movement/drag forces
R: hydrodynamic radius assumingdraf on molecule/particle can be modeled as a sphere

Diffusion is always a function of temperature and viscosity

Fick’s Law

thermal motion of all gases and liquids
movement from higher cenetration to lower
diffusion described by ficks law (don’t need to know on exam, just know overarching concept)— something passing through an area over time ( essentially flow) (concentration gradient is important for flux, negative means movement happens down gradient aka high to low concentration

flux (mol/m²s) = diffusivity (m²/s)*concentration gradient of species (M/m)

dc/dt=-concentration gradient of flux

Flux

something per area per time (molecules, heat, etc)

Are tissues homogenous or heterogeneous (mixed cells or same cells)
approximate them as homogeneous with effective diffusivity

is composed of diffusion, convection, mobility transport

Flux = -D(d[S]/dx) = -D(d[S]/dr)

types of transport

diffusion, convection, mobility

dCi/dt = -concentration gradient(Ji) +Ri

Ji = -Dconcentration gradient(Ci) + (zi/|zi|)uiCiE

= diffusion + convection + mobility

diffusion

movement of indiivdual molecules

convection

Movement of the bulk fluid

Mobility

Movement of charged species by an electric field

Conservation of a species

• choose a region of space

• flow in - flow out + generated - consumed = 0

D for proteins (10-100kDa) in water

10^-6 cm²/s

D for proteins (10-100kDA) in tissues

10^-7 cm²/s = 10-50 um²/s