Lecture 5

Question 1

Linear stability analysis

Answer 1

• Every (continuous) non-linear system can be approximated by a linear set of equations in a “small” interval
• Small scale: walk straight at the beach
• Large scale: curvature -> circular beach

Question 2

Genetic Switch - Phase Portrait

Answer 2

• System can act as a biological switch
• However, slow RNA/protein decay: need ab < 1/2
• Then two states: at origin and high expression level with saddle point as threshold

Question 3

Cell Differentiation Cell Fate Decisions

Answer 3

• How to cells !nd their “dierentiation route” and why do they stay there?
• Cells live in a potential/attractor landscape (Monostable / Bistable / Multistable)
• Generalize positive/negative feedback as causes of cell fate & dierentiation
  => Lateral Inhibition

Question 4

Differentiation Processes with Potential

Answer 4

• Use of Attractor Landscape has strong biological implications

Question 5

Bifurcations in Drosophila Development

Answer 5

• Lateral inhibition Stem cells divide asymmetrically
• Drosophila eggs develop in the germanium
• niche provides renewal factor Decapentaplegic (DPP)
• stem cell divides: one remains in niche, other becoming cytoplast -> gain of Bam expression

Question 6

Establishing a Model for Differentiation

Answer 6

• Dpp is the Drosophila homolog of the vertebrate bone morphogenetic proteins (BMPs),
• Dpp signals through receptor thickveins (Tkv) and transducer Mothers against decapentaplegic (Mad)
• pMad represses key dierentiation factor Bag of marbles (Bam)
• Nos is downregulated by Bam
• Brat Expression is Limited to Dierentiating Cells by Nos
• Brat represses the Dpp Signal Transducer Mad
• Brat mutants lose Bistability

Question 7

Ovarian Stem Cell Niche Model

Answer 7

• GSC: High dMyc Expression -> Dpp uptake & repression of Bam through pMad -> Nos-Pum repress Brat
• Transient loss of Dpp -> differentiation triggered
• Bam represses Nos and Brat expression starts -> loss of Mad