The Influence of Spatial Variation in Chromatin Density Determined by X-Ray Tomograms on the Time to Find DNA Binding Sites

Samuel A. Isaacson, Carolyn A. Larabell, Mark A. Le Gros, David M. McQueen, Charles Peskin

Research output: Contribution to journalArticle

Abstract

In this work, we examine how volume exclusion caused by regions of high chromatin density might influence the time required for proteins to find specific DNA binding sites. The spatial variation of chromatin density within mouse olfactory sensory neurons is determined from soft X-ray tomography reconstructions of five nuclei. We show that there is a division of the nuclear space into regions of low-density euchromatin and high-density heterochromatin. Volume exclusion experienced by a diffusing protein caused by this varying density of chromatin is modeled by a repulsive potential. The value of the potential at a given point in space is chosen to be proportional to the density of chromatin at that location. The constant of proportionality, called the volume exclusivity, provides a model parameter that determines the strength of volume exclusion. Numerical simulations demonstrate that the mean time for a protein to locate a binding site localized in euchromatin is minimized for a finite, nonzero volume exclusivity. For binding sites in heterochromatin, the mean time is minimized when the volume exclusivity is zero (the protein experiences no volume exclusion). An analytical theory is developed to explain these results. The theory suggests that for binding sites in euchromatin there is an optimal level of volume exclusivity that balances a reduction in the volume searched in finding the binding site, with the height of effective potential barriers the protein must cross during the search process.

Original languageEnglish (US)
Pages (from-to)2093-2117
Number of pages25
JournalBulletin of Mathematical Biology
Volume75
Issue number11
DOIs
StatePublished - 2013

Fingerprint

Chromatin
Binding sites
chromatin
spatial variation
binding sites
Euchromatin
X-radiation
DNA
Binding Sites
X-Rays
Proteins
X rays
Heterochromatin
Protein
protein
X Ray Tomography
Olfactory Receptor Neurons
Cell Nucleus Division
heterochromatin
proteins

Keywords

  • First passage time
  • Gene regulation

ASJC Scopus subject areas

  • Neuroscience(all)
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Pharmacology
  • Immunology
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)

Cite this

The Influence of Spatial Variation in Chromatin Density Determined by X-Ray Tomograms on the Time to Find DNA Binding Sites. / Isaacson, Samuel A.; Larabell, Carolyn A.; Le Gros, Mark A.; McQueen, David M.; Peskin, Charles.

In: Bulletin of Mathematical Biology, Vol. 75, No. 11, 2013, p. 2093-2117.

Research output: Contribution to journalArticle

Isaacson, Samuel A. ; Larabell, Carolyn A. ; Le Gros, Mark A. ; McQueen, David M. ; Peskin, Charles. / The Influence of Spatial Variation in Chromatin Density Determined by X-Ray Tomograms on the Time to Find DNA Binding Sites. In: Bulletin of Mathematical Biology. 2013 ; Vol. 75, No. 11. pp. 2093-2117.
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