Patterns DDI

Question 1

What is morphogenesis?

Answer 1

The biological process that generates shape and form.

Question 2

What is a biological pattern?

Answer 2

A stable, spatially non-uniform steady state.

Question 3

What are morphogens?

Answer 3

Substances controlling pattern formation via gradients.

Question 4

What is a reaction–diffusion system?

Answer 4

A model combining reaction kinetics and diffusion.

Question 5

What is diffusion-driven instability?

Answer 5

Diffusion destabilising a uniform steady state.

Question 6

What is a wave number, k?

Answer 6

Measure of spatial frequency.

Question 7

What does k=0 represent?

Answer 7

Uniform perturbation.

Question 8

What does k>0 represent?

Answer 8

Spatial perturbation.

Question 9

Why two species required?

Answer 9

Single species cannot pattern.

Question 10

What is an activator?

Answer 10

Species that promotes its own production.

Question 11

What is an inhibitor?

Answer 11

Species that suppresses growth.

Question 12

Why unequal diffusion?

Answer 12

Necessary for Turing patterns. D_u =! D_v

Question 13

What are no-flux boundaries?

Answer 13

Zero spatial derivative at edges.

Question 14

Why biological boundaries no-flux?

Answer 14

No movement across tissue edge.

Question 15

What is the general RD equation?

Answer 15

∂U/∂t = D∇²U + F(U).

Question 16

What does U represent?

Answer 16

Vector of concentrations.

Question 17

What does D represent?

Answer 17

Diffusion matrix.

Question 18

Why D diagonal?

Answer 18

Independent diffusion.

Question 19

What does F(U) represent?

Answer 19

Reaction kinetics.

Question 20

What is dispersion relation?

Answer 20

λ as function of k².

Question 21

What is fastest growing mode?

Answer 21

Mode with maximum λ.

Question 22

Why fastest mode matters?

Answer 22

Predicts observed pattern.

Question 23

What does domain length affect?

Answer 23

Allowed k values.

Question 24

What must hold without diffusion?

Answer 24

Uniform state stable.

Question 25

What conditions ensure stability at k=0?

Answer 25

tr(M)<0, det(M)>0.

Question 26

What indicates instability k, h?

Answer 26

Instability for some k>0. h'(0) <0 Min(h(k2)) < 0 b^2 > 4ac

Question 27

What is h(k²)?

Answer 27

det(M − k²D).

Question 28

Why h(k²)<0 important?

Answer 28

Necessary for instability h(k²) is det so < 0 for instability

Question 29

What is λmax?

Answer 29

Maximum growth rate.

Question 30

Why λmax important?

Answer 30

Determines pattern scale.

Question 31

What ansatz to use after linearising a 2d system which now looks like dz/dt = D d2z/dE2 +Mz

Answer 31

w(E, t) = w(E) e^(lambda t) then w(E) = e^(ikE) w_0