A Hybrid HMM Approach for the Dynamics of DNA Methylation - - PowerPoint PPT Presentation

A Hybrid HMM Approach for the Dynamics

• f DNA Methylation

Charalampos Kyriakopoulos, Pascal Giehr, Alexander L¨ uck, J¨

• rn Walter, Verena Wolf

HSB 2019 6th Workshop on Hybrid Systems & Biology April 06, 2019

Introduction Model Results

Importance of Epigenetics

Every cell contains the whole genome and therefore the ”blueprints” for all producible proteins. DNA skin heart brain lung . . . How can cells specialize? Why do some cells develop diseases? DNA healthy cancer . . .

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Introduction Model Results

DNA Methylation

. . . T A C G C C C T G T C G A. . . . . . A T G C G G G A C A G C T. . . Occurs (almost exclusively) on cytosine in CpGs (DNA sequence: C - Phosphor - G) DNA methyltransferases (Dnmts) convert cytosine (C) to 5-methylcytosine (5mC) C 5mC Methylated cytosine hinders transcription of DNA into mRNA

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Introduction Model Results

Methylation and further modifications

cytosine (C):

• riginal unmodified base in DNA

5-methylcytosine (5mC): methylated C → gene inactivation 5-hydroxymethylcytosine (5hmC): hydroxymethylated C → gene activation 5-formylcytosine (5fC): formylated C → active demethylation

C C C C

CH3 CH2OH CHO DNMT Tet Tet

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Introduction Model Results

Passive and active demethylation

Passive demethylation: Losing methylation over time due to cell division and failed maintenance and/or decreasing methylation efficiency. Active demethylation: 5hmC 5mC 5fC C η φ δ µ

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Introduction Model Results

Motivation

1 Incorporate different types of event classes in the model:

Events that only occur once at deterministic times (discrete; cell division and maintenance) and events that may occur more than once at random times (continuous; methylation cycle). → Existing models are either exclusively discrete or continuous.

2 Model and predict levels of 5fC.

→ Important for active demethylation.

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Introduction Model Results

Modeling of (de)methylation events

Modeling via Hidden Markov Model with 16 hidden states (4 methylation states on double-stranded DNA) and 4 observable states (2 for each strand). A detailed look into the individual processes:

? ? ? ?

Cell division: Keep one strand as it is and synthesize a new complementary strand with only unmethylated cytosines. Strand to keep is chosen randomly with probability 0.5.

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Introduction Model Results

Maintenance methylation

μm μm

Maintenance methylation

• nly on hemi-methylated

CpGs (rate µm) right after cell division. Assumption based

• n

previous results: No maintenance

• n

hemi-hydroxylated and hemi-formylated CpGs States: C, 5mC, 5hmC, 5fC

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Introduction Model Results

Continuous transitions

The reactions de novo µd hydroxylation η formylation φ demethylation δ may

• ccur

more than once in each cell division cycle. States: C, 5mC, 5hmC, 5fC

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Introduction Model Results

Model dynamics

Discrete transitions at fixed times t ∈ {t1, t2, . . . , tn}: Cell division and maintenance (linked to replication fork) → DTMC with transition probability matrix P Continuous transitions at random times t ∈ [ti, ti+1]: Transitions within the methylation cycle (de novo, hydroxylation, formylation, active demethylation) → CTMC with infinitesimal generator matrix Q

t1 t2 t3 t4 probability

Q Q Q Q Q P P P P 9

Introduction Model Results

Efficiencies

Let r ∈ {µm, µd, η, φ, δ}, where µm is a transition probability and µd, η, φ, δ are transition rates. Time dependent efficiencies, due to e.g. changing enzyme concentrations: r(t) := αr + βr · t Introduce bounds in order to ensure identifiability: 0 ≤ r(t) ≤ ub Choose ub based on biological assumptions → prohibit arbitrarily fast reactions

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Introduction Model Results

Hidden and observable states

Hidden states: C, 5mC, 5hmC and 5fC Observable states: C and T

BS

• xBS

MAB-Seq C C 5mC 5hmC 5fC C 5mC 5hmC 5fC C 5mC 5hmC 5fC T C C T T C T T T C C T c d e g c d f g c d e g m 11

Introduction Model Results

Data

Example data set: Data for single copy gene Afp (alpha fetoprotein) containing 5

• CpGs. Three data sets (BS, oxBS and MAB-Seq) to identify

hidden states. Parameter estimation via MLE. Similar results for all 5 CpGs ⇒ Show only aggregated results in the following.

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Introduction Model Results

Observable states

1 3 6

day

0.2 0.4 0.6 0.8 1

frequency BS

TT TT pr TC TC pr CT CT pr CC CC pr

1 3 6

day

0.2 0.4 0.6 0.8 1

• xBS

1 3 6

day

0.2 0.4 0.6 0.8 1

MAB-Seq

Good agreement between data (solid lines) and results from the model (dashed lines).

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Introduction Model Results

Hidden states

day0 day1 day3 day6 0.2 0.4 0.6 0.8 1

level per states

day0 day1 day3 day6 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

hydroxylation level

hm-mh uh-hu hh day0 day1 day3 day6 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

5fC level

mf-fm uf-fu hf-fh ff

unmethylated fully methylated hemimethylated hydroxy formal

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Introduction Model Results

Efficiencies

1 2 3 4 5 6

day

0.2 0.4 0.6 0.8 1

efficiency

μm μd η ϕ δ

Measured time points too far apart (only one measurement for each cell division cycle) ⇒ How often was the methylation cycle traversed? No information about intermediate time points.

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Introduction Model Results

Summary

Hybrid HMM (discrete for cell division and maintenance; continuous for methylation cycle events) Very flexible model (choice of time points for discrete events, efficiency function) Good prediction performance, however available data is not ideal so far

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Introduction Model Results

Thank you for your attention!

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