Chromatin structure A mathematical model for silencing in yeast Bibliography Mathematical Epigenetics Mathematical modeling of chromatin silencing Amirhossein Hajihosseini Center of Excellence in Biomathematics School 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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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)
Chromatin structureA mathematical model for silencing in yeast
Bibliography
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.
Chromatin structureA mathematical model for silencing in yeast
Bibliography
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.
Chromatin structureA mathematical model for silencing in yeast
Bibliography
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.
Chromatin structureA mathematical model for silencing in yeast
Bibliography
Thank you
Amirhossein Hajihosseini
Research AssistantCenter of Excellence in BiomathematicsSchool of Mathematics, Statistics and Computer ScienceUniversity of Tehran, Tehran 14176-14411, Iran