Parameter inference of a basic p53 model using ABC

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Parameter inference of a basic p53 model using ABC

Eszter Lakatos and Michael Barclay

Group meeting 29th _{October 2014}

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Background

Study p53 reaction to cellular stress on single cell level

Compare and model (stochastically) normal and drug-treated cells

MCF-7 cells

human breast cancer cell line

BE cells

bigger cells, faster growth

Actinomycin D

polypeptide antibiotic with anti-cancer activity transcriptional inhibitor

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Experimental results

0 1.5 3 4.5 6 x 104 5 10 15 20 80nM ActinomycinD (n = 65) 0 1 2 3 4 5 x 104 5 10 15 20 25 40nM ActinomycinD (n = 58) 0 4 8 12 x 105 4 8 12 16 BE cells (n = 51) 0 0.4 0.8 1.2 1.6 2 x 104 5 10 15 20 25 MCF7 cells (n = 45) 0 0.75 1.5 2.25 3 x 104 10 20 30 40 8nM ActinomycinD (n = 69)

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Model

˙ m=k1−k2m ˙ p =k3m−k4p k₁ - transcription k₂ - mRNA degr. k₃ - translation k₄ - protein degr.

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Model

˙ m=k1−k2m ˙ p =k3m−k4p k₁ - transcription k₂ - mRNA degr. k₃ - translation k₄ - protein degr.

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Combined model of different cell populations

MCF7: ˙ m1=k1−k2m1 ˙ p1=k3m1−k4p1 k₁ - transcription k₂ - mRNA degr. k₃ - translation k₄ - protein degr. BE: ˙ m2 =k1s−k2sm2 ˙ p2=k3sm2−k4sk5p2 s - scaling factor k₅ - modifier Hypothesis: k5<<1

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Combined model of different cell populations

8nM ActD: ˙ m1 =k1−k2m1 ˙ p1 =k3m1−k4p1 k₁ - transcription k₂ - mRNA degr. k₃ - translation k₄ - protein degr. 40nM ActD: ˙ m2 =k1−k2m2 ˙ p2 =k3m2−k5p2 k₅ - protein degr. 80nM ActD: ˙ m3 =k1−k2m3 ˙ p3 =k3m3−k6p3 k₆ - protein degr. Hypothesis: k6 <k5<k4

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Inference using ABC

Algorithm

Sample parameters from (prior) distribution

Simulate each particle n times: SDE

Compare experimental and simulated populations

Accept particle if distance<

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Inference using ABC

Algorithm

Sample parameters from (prior) distribution

Simulate each particle n times: SDE

Compare experimental and simulated populations

Accept particle if distance<

Iterate

Conclusions from the first months:

Kolmogorov-Smirnov distance

Non-identifiability

Rescale parameters by settingk₂=1

Check the limitations with simulated experimental data

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Results I. - Identifiability

Populations (n=60) simulated with the same parameters

0 5000 10000 15000 20000 25000 0.0 0.2 0.4 0.6 0.8 1.0 sim. experimental simulation0 simulation1 0 5000 10000 15000 20000 0 5 10 15 2025 3035

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Results I. - Identifiability

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Results I. - Identifiability

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Results I. - Identifiability

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Results I. - Identifiability

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Combined model of different cell populations

MCF7: ˙ m1=k1−k2m1 ˙ p1=k3m1−k4p1 k₁ - transcription k₂ - mRNA degr. k₃ - translation k₄ - protein degr. BE: ˙ m2 =k1s−k2sm2 ˙ p2=k3sm2−k4sk5p2 s - scaling factor k₅ - modifier Hypothesis: k5<<1

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Combined model of different cell populations

8nM ActD: ˙ m1 =k1−k2m1 ˙ p1 =k3m1−k4p1 k₁ - transcription k₂ - mRNA degr. k₃ - translation k₄ - protein degr. 40nM ActD: ˙ m2 =k1−k2m2 ˙ p2 =k3m2−k5p2 k₅ - protein degr. 80nM ActD: ˙ m3 =k1−k2m3 ˙ p3 =k3m3−k6p3 k₆ - protein degr. Hypothesis: k6 <k5<k4

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Results II. - Real data

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Results II. - Real data

Combined model of MCF7 and BE cells

0 5000 10000 15000 20000 0.0 0.2 0.4 0.6 0.8 1.0 0 200000 400000 600000 800000 1000000 1200000 0.0 0.2 0.4 0.6 0.8 1.0 simulation1 simulation2 experimental

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Results II. - Real data

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Results II. - Real data

Combined model of 3 doses of ActinomycinD treatment

0 5000 10000 15000 20000 25000 30000 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 50000 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 50000 60000 70000 0.0 0.2 0.4 0.6 0.8 1.0 simulation1 simulation2 experimental

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Results II. - Real data

Combined models of 3 doses of ActinomycinD treatment Model 1: ActD affects protein degradation

Model 2: ActD affects transcription Model 3: ActD affects translation

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Results II. - Real data

Combined models of 3 doses of ActinomycinD treatment

0 5000 10000 15000 20000 25000 30000 0.0 0.2 0.4 0.6 0.8 1.0 0 10000 20000 30000 40000 50000 60000 0.0 0.2 0.4 0.6 0.8 1.0 0 20000 40000 60000 80000 100000 120000 0.0 0.2 0.4 0.6 0.8 1.0 simulation13 simulation83 simulation98 experimental

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Plans, problems, questions

More data (faster set-up)

Fluorescent data from MCF7 and BE cells

Both p53 and Mdm2 labelling

Low molecular numbers of protein are not measured reliably

E.g. in the MCF7 cell line, about 10 cells were thrown out

Can be considered in distance

Two populationsof cells