1. Alexis Carulli CCB Project Notch Regulation of Intestinal Crypt Dynamics

2. The Intestinal Crypt: Proliferative Zone Transit-Amplifying Progenitor(TA) Stem Cell Notch?

3. Experimental ObservationsHypothesis Asymmetric Cell Division Symmetric Cell Division Notch Inhibition 5 day Notch inhibition 1 day Notch inhibition

4. Continuous Compartmental Model of Crypt Dynamics α1α1 α2α2 α3α3 β1β1 β2β2 β3β3 γ apoptosis renewal differentiation sloughing-off N 0 Stem N 1 TA N 2 Diff WITH FEEDBACK: = (α 3 – α 1 – α 2 )N 0 – k 0 N 2 0 1 + m 0 N 0 dN 0 dt k 0 N 2 0 1 + m 0 N 0 = (β 3 – β 1 – β 2 )N 1 – k 1 N 2 1 1 + m 1 N 1 dN 1 dt + α 2 N 0 + = – γN 2 + β 2 N 1 + k 1 N 2 1 1 + m 1 N 1 dN 2 dt Johnston et al. PNAS 2007

5. Continuous Compartmental Model of Crypt Dynamics α1α1 α2α2 α3α3 β1β1 β2β2 β3β3 γ apoptosis renewal differentiation sloughing-off N 0 Stem N 1 TA N 2 Diff WITH FEEDBACK: = (α 3 – α 1 – α 2 )N 0 – k 0 N 2 0 1 + m 0 N 0 dN 0 dt k 0 N 2 0 1 + m 0 N 0 = (β 3 – β 1 – β 2 )N 1 – k 1 N 2 1 1 + m 1 N 1 dN 1 dt + α 2 N 0 + = – γN 2 + β 2 N 1 + k 1 N 2 1 1 + m 1 N 1 dN 2 dt Johnston et al. PNAS 2007

6. Continuous Model: α 2 and α 3 analysis 1 day Notch inhibition5 day Notch inhibition α 2 = 1 α 3 = 0 α 2 = 3 α 3 = 0.586 Homeostatic rates: α 2 = 0.3, α 3 = 0.586 α 2 = 5 α 3 = 0.001 N2N2 N0N0 N1N1

7. Continuous Compartmental Model of Crypt Dynamics α1α1 α2α2 α3α3 β1β1 β2β2 β3β3 γ apoptosis renewal differentiation sloughing-off N 0 Stem N 1 TA N 2 Diff Even if N 0 =0 there is still a population of N 1 and N 2 cells: Johnston et al. PNAS 2007 N2N2 N0N0 N1N1

8. Continuous Model: β 3 analysis Homeostatic rate: β 3 = 0.732 1 day Notch inhibition5 day Notch inhibition Β 3 = 0 α 2 = 1 α 3 = 0.3

9. D (t+1) = D + 0.6T 2 – γ T1 (t+1) = 3XSTT (t+1) = T 1 + T 2 T2 (t+1) = 4T 1 S (t+1) = S + (1-X)S + R Discrete Compartmental Model of Crypt Dynamics X R γ ASSUMPTION: When crypt is in homeostasis, apoptosis is negligible in S and T compartments renewal differentiation amplification Slough off S Stem T 1 TA D Diff T 2 TA differentiation X= Stem cell division symmetry X=0: completely symmetric, towards S X=1: completely asymmetric, equal S and TT X=2: completely symmetric, towards TT

10. Discrete Model: X analysis X=0 X=1 X=2 Maximum is 60% increased from TT i NOTE: In my experiment I saw a 60% increase in proliferating cells after 1 day of Notch inhibition S grows exponentially, TT crashes Homeostasis TT S

11. Discrete Model; x=1.5 1 day Notch inhibition5 day Notch inhibition No stem cell renewal Constant stem cell renewal Notch- dependent stem cell renewal TT S

12. Discrete Model: Alternate hypothesis Notch inhibition may result in stem cell apoptosis and the rebound stem cell overpopulation, without affecting differentiation rate of S  TT 1 day Notch inhibition 5 day Notch inhibition TT S Stem cell loss Stem cell rebound

13. Future Directions X R γ S Stem T 1 TA D Diff T 2 TA T 3 TA T 4 TA 1) Test different permutations of amplification scheme 2) Design hybrid model - Neither discrete nor continuous is likely correct - Adapt discrete model to ODEs with feedback, but maintain dependence on S compartment 3) Do more experiments! - Check intermediate time points for proliferation drop

14. Thanks! Many thanks to the course instructors (Especially Greg!) and the TAs. It was great to meet all of you. Safe travels home and may you have many Science/Nature/Cell publications in the future