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
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Chromatin structureA mathematical model for silencing in yeast
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Overwiev
1 Chromatin structure
2 A mathematical model for silencing in yeast
3 Bibliography
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Chromatin structureA mathematical model for silencing in yeast
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Chromatin structure
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Chromatin structureA mathematical model for silencing in yeast
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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 structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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DNA configuration in eukaryotic cells
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Chromatin structureA mathematical model for silencing in yeast
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DNA configuration in eukaryotic cells
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Chromatin structureA mathematical model for silencing in yeast
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DNA configuration in eukaryotic cells
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Chromatin structureA mathematical model for silencing in yeast
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DNA configuration in eukaryotic cells
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Chromatin structureA mathematical model for silencing in yeast
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DNA configuration in eukaryotic cells
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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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Post-translational histone modifications
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Chromatin structureA mathematical model for silencing in yeast
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A mathematical modelfor silencing in yeast
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Chromatin structureA mathematical model for 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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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Bibliography
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Chromatin structureA mathematical model for silencing in yeast
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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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Chromatin structureA mathematical model for silencing in yeast
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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
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