mathematical epigenetics - mathematical modeling of chromatin

Chromatin structureA mathematical model for silencing in yeast

Bibliography

Mathematical EpigeneticsMathematical modeling of chromatin silencing

Amirhossein Hajihosseini

Center of Excellence in BiomathematicsSchool of Mathematics, Statistics and Computer Science

University of Tehran

2nd Workshop on Biomathematics

School of Mathematics, Institute for Research in Fundamental Sciences (IPM)

December 26, 2011

Amirhossein Hajihosseini Mathematical Epigenetics 1 / 20


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Overwiev

1 Chromatin structure

2 A mathematical model for silencing in yeast

3 Bibliography



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Chromatin structure



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DNA structure

DNA is a long double-stranded helical macromolecule in which the genetic

information in living cells is stored. This information is called the genome. In each

strand, the genome is encoded by four alternating units called nucleotides. More

specifically, each strand of DNA contains a repeating sugar/phosphate backbone

and a base attached to each sugar unit. These bases are chosen from the four

organic components of adenine (A), cytosine (C), guanine (G) and thymine (T).



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Chromatin

Chromatin and higher order chromosome structures play a central role in nearlyevery aspect of DNA biology in eukaryotes. Chromatin is referred to the highlycomplex mixture of DNA and structural proteins (histones).

During interphase, eukaryotic chromatin is divided into two distinct regions:

Heterochromatin:

. Highly condensed and packed

. Transcriptionally inactive

Euchromatin:

. Less compact

. Transcriptionally active

Heterochromatin formation plays a crucial role in multicellular development by

stabilizing gene expression patterns in specialized cells.



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The nucleosome

The nucleosome is the building block of chromatin that is composed of an octamer

of the four highly basic core histones (H3, H4, H2A, and H2B) plus a linker

histone (H1) around which 147 base pairs of DNA are wrapped.



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DNA configuration in eukaryotic cells



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Histones & N-terminal tails

Each histone protein has an N-terminal tail. These tails provide a guide for the

DNA strand to wrap around the histone core. The N-terminal tails emerge

between the DNA strands and create a groove that forces the DNA to wrap in a

left-handed manner around the histone.



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Histone modifications on histone tails

[E. Habibi, A. Masoudi-Nejad, H. M. Abdolmaleky, S. J. Haggarty, 2011]



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Examples of histone modifications & their role in transcriptionregulation

Histone acetylation Activation

Histone deacetylation Repression

Histone methylation Activation/Repression

Histone demethylation Activation/Repression

Histone phosphorylation Activation

Histone ubiquitylation Activation/Repression



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Epigenetic mechanisms

Although all cells have the same genetic information, different regions of genome

may be silenced in different cells.

Same genotype, different phenotypes.

Inheritable differences in cellular behavior or phenotype, despite having thesame genetic information, is called epigenetic phenomena. Therefore,epigenetics can be summarized to include the structural adaptation ofchromosomal regions so as to register, signal or perpetuate altered activitystates.

Inheritable changes in gene function and expression that don’t involvechanges in DNA sequence are commonly referred to as epigenetic. Theseinclude rapid adjustments of gene expression in response to physiologicaland environmental stimuli as well as more permanent indexing system whichcould be involved in transmitting inheritable expression patterns from onecell generation to the next.



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Post-translational histone modifications



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A mathematical modelfor silencing in yeast



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The silencing mechanism in yeast

Nucleation: Site-specific binding proteins and Sir1 help Sir2, Sir3 and Sir4 form

a Sir complex on the nucleation site. Binding of Sir3/Sir4 complex in the

neighborhood of the original nucleation site will then become easier when certain

lysines on the neighboring histones H3 and H4 are deacetylated by Sir2.

[M. Sedighi, A. Sengupta, 2007]



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The silencing mechanism in yeast

Spreading: Sir3/Sir4 complex recruits more Sir2. The recruitment of other Sir

proteins will be improved when histone tails are more dacetylated. This results in

spreading of silencing.

[M. Sedighi, A. Sengupta, 2007]



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The mathematical model

The main variables for a mathematical model for the silencing mechanism are:

The local probability of occupation by Sir complex

. Si(t): the fractional number of Sir complexes at site i

The local degree of acetylation

. Ai(t): the fractional degree of acetylation at site i



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The mathematical model

dSi(t)

dt= ρi(t)

(1− Si(t)

)f(

1−Ai(t))− ηSi(t)

dAi(t)dt

= α(

1−Ai(t))(

1− Si(t))−(λ+ ΣjγijSj(t)

)Ai(t)

ρi(t) is the 3D concentration of ambient Sir complex at site i.

α denotes the constant acetylation rate.

η represents the degradation rate of bound Sir complexes.

λ is the rate of deacetylation from the rest of acetylase proteins.

γij is assumed to be symmetric with respect to its indeces and dropsignificantly as |i− j| gets larger.

The function f(x) = xn indicates the cooperativity in Sir complex binding;n is the degree of cooperativity between deacetylated histone tails inrecruiting Sir proteins.



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Bibliography

Bibliography

1© S. I. Grewal, D. Moazed.Heterochromatin and Epigenetic Control of Gene Expression.Science 301 (2003) 798-802.

2© E. Habibi, A. Masoudi-Nejad, H. M. Abdolmaleky, S. J. Haggarty.Emerging roles of epigenetic mechanisms in Parkinson’s disease.Funct Integr Genomics 11 (2011) 523-537.

3© M. Sedighi.THE PHYSICS OF CHROMATIN SILENCING: BI-STABILITY ANDFRONT PROPAGATION.PhD Thesis, Rutgers, The State University of New Jersey, 2007.

4© M. Sedighi, A. M. Sengupta.Epigenetic chromatin silencing: bistability and front propagation.Phys Biol. 4 (2008) 246-255.



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Thank you

Amirhossein Hajihosseini

Research AssistantCenter of Excellence in BiomathematicsSchool of Mathematics, Statistics and Computer ScienceUniversity of Tehran, Tehran 14176-14411, Iran

[email protected]@gmail.com


mathematical epigenetics - mathematical modeling of chromatin

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