Mathematical model of alternative mechanism of telomere length maintenance Journal Article


Author(s): Kollár, Richard; Bod'ová, Katarína; Nosek, Jozef; Tomáška, Ľubomír
Article Title: Mathematical model of alternative mechanism of telomere length maintenance
Affiliation IST Austria
Abstract: Biopolymer length regulation is a complex process that involves a large number of biological, chemical, and physical subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres - nucleoprotein structures at the ends of linear chromosomes consisting of tandemly repeated DNA sequences and a specialized set of proteins. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination. Various linear and circular DNA structures were identified to participate in ALT, however, dynamics of the whole process is still poorly understood. We propose a chemical kinetics model of ALT with kinetic rates systematically derived from the biophysics of DNA diffusion and looping. The reaction system is reduced to a coagulation-fragmentation system by quasi-steady-state approximation. The detailed treatment of kinetic rates yields explicit formulas for expected size distributions of telomeres that demonstrate the key role played by the J factor, a quantitative measure of bending of polymers. The results are in agreement with experimental data and point out interesting phenomena: an appearance of very long telomeric circles if the total telomere density exceeds a critical value (excess mass) and a nonlinear response of the telomere size distributions to the amount of telomeric DNA in the system. The results can be of general importance for understanding dynamics of telomeres in telomerase-independent systems as this mode of telomere maintenance is similar to the situation in tumor cells lacking telomerase activity. Furthermore, due to its universality, the model may also serve as a prototype of an interaction between linear and circular DNA structures in various settings.
Keywords: Kinetics; MATHEMATICAL MODELS; Dna; Quantitative measures; Maintenance; Size distribution Chemical kinetics model; Non-linear response; Quasi steady state approximation; Repeated DNA sequences; Spatial and temporal scale; Telomerase activity; Telomere maintenance: Chromosomes
Journal Title: Physical Review E Statistical Nonlinear and Soft Matter Physics
Volume: 89
Issue 3
ISSN: 1539-3755
Publisher: American Institute of Physics  
Date Published: 2014-03-04
Start Page: Article number 032701
Sponsor: The work was supported by Marie Curie International Reintegration Grant No. 239429 from the European Commission (R.K.), by the VEGA Grant No. 1/0459/13 (R.K. and K.B.), and by Grants No. APVV-0123-10 and No. APVV-0035-11 from the Slovak Research and Devel
URL:
DOI: 10.1103/PhysRevE.89.032701
Open access: yes (repository)