Alexis CarulliCCB Project

Notch Regulation of Intestinal Crypt Dynamics

The Intestinal Crypt: Proliferative Zone

Transit-AmplifyingProgenitor(TA)

Stem CellNotch?

Experimental Observations HypothesisAsymmetric Cell Division

Symmetric Cell Division

Notch Inhibition

5 day Notch inhibition1 day Notch inhibition

Continuous Compartmental Model of Crypt Dynamics

α1

α2

α3

β1

β2

β3

γ

apoptosis apoptosis

renewal renewal

differentiation differentiation sloughing-off N0Stem

N1TA

N2Diff

WITH FEEDBACK: = (α3 – α1 – α2)N0 –

k0N20

1 + m0N0

dN0

dt

k0N20

1 + m0N0 = (β3 – β1 – β2)N1 –

k1N21

1 + m1N1

dN1

dt + α2N0 +

= – γN2 + β2N1 + k1N2

1 1 + m1N1

dN2

dt

Johnston et al. PNAS 2007

Continuous Compartmental Model of Crypt Dynamics

α1

α2

α3

β1

β2

β3

γ

apoptosis apoptosis

renewal renewal

differentiation differentiation sloughing-off N0Stem

N1TA

N2Diff

WITH FEEDBACK: = (α3 – α1 – α2)N0 –

k0N20

1 + m0N0

dN0

dt

k0N20

1 + m0N0 = (β3 – β1 – β2)N1 –

k1N21

1 + m1N1

dN1

dt + α2N0 +

= – γN2 + β2N1 + k1N2

1 1 + m1N1

dN2

dt

Johnston et al. PNAS 2007

Continuous Model: α2 and α3 analysis

1 day Notch inhibition 5 day Notch inhibition

α2 = 1α3 = 0

α2 = 3α3 = 0.586

Homeostatic rates: α2 = 0.3, α3 = 0.586

α2 = 5α3 = 0.001

N2

N0

N1

Continuous Compartmental Model of Crypt Dynamics

α1

α2

α3

β1

β2

β3

γ

apoptosis apoptosis

renewal renewal

differentiation differentiation sloughing-off N0Stem

N1TA

N2Diff

Even if N0=0 there is still a population of N1 and N2 cells:

Johnston et al. PNAS 2007

N2

N0

N1

Continuous Model: β3 analysisHomeostatic rate: β3 = 0.732

1 day Notch inhibition 5 day Notch inhibition

Β3 = 0α2 = 1α3 = 0.3

D(t+1) = D + 0.6T2 – γ

T1(t+1) = 3XS TT(t+1) = T1 + T2

T2(t+1) = 4T1

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 Sloughoff S

Stem T1TA

DDiff

T2TA

differentiation

X= Stem cell division symmetryX=0: completely symmetric, towards SX=1: completely asymmetric, equal S and TTX=2: completely symmetric, towards TT

Discrete Model: X analysis

X=0

X=1

X=2Maximum is 60% increased from TTi

NOTE: In my experiment I saw a 60% increase in proliferating cells after 1 day of Notch inhibition

S grows exponentially, TT crashes

Homeostasis

TTS

Discrete Model; x=1.5 1 day Notch inhibition 5 day Notch inhibition

No stem cell renewal

Constant stem cell renewal

Notch-dependent stem cell renewal

TTS

Discrete Model: Alternate hypothesis

Notch inhibition may result in stem cell apoptosis and the rebound stem cell overpopulation, without affecting differentiation rate of

STT

1 day Notch inhibition 5 day Notch inhibitionTTS

Stem cell loss

Stem cell rebound

Future Directions

X

R

γS

Stem T1TA

DDiff

T2TA

T3TA

T4TA

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

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