7 Reaction-Diffusion Model (Turing Patterns) Flashcards
What is the chemical basis of morphogenesis?
Morphology = how an organism is forming its shape
A system may be initially homogeneous but develop a pattern/structure due to an instability of homogeneous equilibrium, triggered by random disturbances
6 different forms of instability
Write the equation for compound’s concentration change over time
Rate of change can be written as a function of concentration c and rate constant k
dc/dt = kc ( 1 - c ) = f(c)
What is Fick’s first law?
Diffusion flux (D) is proportional to conc gradient (dc/dx)
What do the dynamics of concentration c depend on?
Where you are in the gradient = position x
How long it has been diffusing = time
Write the partial differential equation (PDE)
J = -D∇c
This equation explains diffusion in 2D or higher dimension
What is Fick’s second law?***
Diffusion causes concentration to change over time, depending on the change of gradient
What variables affect the rate of concentration change in 2D?
Spatial coordinates x and y
Time t
What is the equation for diffusion in 2D?
D∇^2c = dc(x,y,t) / dt
The dc/dt will be partial differential equations so will have Del
What is the effect of diffusion on the system?
Diffusion tends to equalize the system = causes patterns to be lost because evens out the different between two areas
Homogenizing procedure
What is the equation for reaction-diffusion ?
Partial differential equation
c dot = f(c) + D∇^2c
How does the 2 species reaction-diffusion model evolve ***
Name the 6 stable states of pattern emergence
Uniform, stationary & oscillation
Stationary waves with short wavelength
Oscillatory cases with extremely short wavelength
Oscillatory cases with finite wavelength
Stationary wave with finite wavelength (Turing pattern)
Explain oscillatory cases with finite wavelength
