Mathematical Biosciences and Engineering (MBE)

Mathematical analysis and modeling of DNA segregation mechanisms
Pages: 429 - 440, Issue 2, April 2018

doi:10.3934/mbe.2018019      Abstract        References        Full text (605.9K)           Related Articles

Bashar Ibrahim - Department of Mathematics and Computer Science, University of Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany (email)

1 S. F. Bakhoum, G. Genovese and D. A. Compton, Deviant kinetochore microtubule dynamics underlie chromosomal instability, Curr Biol, 19 (2009), 1937-1942.
2 A. K. Caydasi, B. Ibrahim and G. Pereira, Monitoring spindle orientation: Spindle position checkpoint in charge, Cell Div, 5 (2010), p28.
3 A. K. Caydasi, B. Kurtulmus, M. I. L. Orrico, A. Hofmann, B. Ibrahim and G. Pereira, Elm1 kinase activates the spindle position checkpoint kinase Kin4, J Cell Biol, 190 (2010), 975-989.
4 A. K. Caydasi, M. Lohel, G. Grünert, P. Dittrich, G. Pereira and B. Ibrahim, A dynamical model of the spindle position checkpoint, Mol Syst Biol, 8 (2012), p582.
5 L. M. Cherry, A. J. Faulkner, L. A. Grossberg and R. Balczon, Kinetochore size variation in mammalian chromosomes: An image analysis study with evolutionary implications, J Cell Sci, 92 (1989), 281-289.
6 E. J. Doedel, AUTO: A program for the automatic bifurcation analysis of autonomous systems, Congr Numer, 30 (1981), 265-284.       
7 A. Doncic, E. Ben-Jacob and N. Barkai, Evaluating putative mechanisms of the mitotic spindle checkpoint, Proc Natl Acad Sci U S A, 102 (2005), 6332-6337.
8 B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students, (society for industrial and applied mathematics, philadelphia), 2002.       
9 D. Görlich, G. Escuela, G. Gruenert, P. Dittrich and B. Ibrahim, Molecular codes through complex formation in a model of the human inner kinetochore, Biosemiotics, 7 (2014), p223.
10 G. Gruenert, B. Ibrahim, T. Lenser, M. Lohel, T. Hinze and P. Dittrich, Rule-based spatial modeling with diffusing, geometrically constrained molecules, BMC Bioinf, 11 (2010), p307.
11 G. Gruenert, J. Szymanski, J. Holley, G. Escuela, A. Diem, B. Ibrahim, A. Adamatzky, J. Gorecki and P. Dittrich, Multi-scale modelling of computers made from excitable chemical droplets, IJUC, 9 (2013), 237-266.
12 R. Henze, J. Huwald, N. Mostajo, P. Dittrich and B. Ibrahim, Structural analysis of in silico mutant experiments of human inner-kinetochore structure, Bio Systems, 127 (2015), 47-59.
13 B. Ibrahim, In silico spatial simulations reveal that MCC formation and excess {BubR1} are required for tight inhibition of the anaphase-promoting complex, Mol Biosyst, 11 (2015), 2867-2877.
14 B. Ibrahim, Spindle assembly checkpoint is sufficient for complete Cdc20 sequestering in mitotic control, Comput Struct Biotechnol J, 13 (2015), 320-328.
15 B. Ibrahim, Systems biology modeling of five pathways for regulation and potent inhibition of the anaphase-promoting complex (APC/C)}: Pivotal roles for MCC and BubR1, Omics, 19 (2015), 294-305.
16 B. Ibrahim, Toward a systems-level view of mitotic checkpoints, Prog Biophys Mol Biol, 117 (2015), 217-224.
17 B. Ibrahim, A mathematical framework for kinetochore-driven activation feedback in the mitotic checkpoint, Bull Math Biol, 79 (2017), 1183-1200.       
18 B. Ibrahim, S. Diekmann, E. Schmitt and P. Dittrich, In-silico modeling of the mitotic spindle assembly checkpoint, PLoS One, 3 (2008), e1555.
19 B. Ibrahim, P. Dittrich, S. Diekmann and E. Schmitt, Stochastic effects in a compartmental model for mitotic checkpoint regulation, J Integr Bioinform, 4 (2007), 77-88.
20 B. Ibrahim, P. Dittrich, S. Diekmann and E. Schmitt, Mad2 binding is not sufficient for complete Cdc20 sequestering in mitotic transition control (an in silico study), Biophys Chem, 134 (2008), 93-100.
21 B. Ibrahim and R. Henze, Active transport can greatly enhance Cdc20:Mad2 formation, Int J Mol Sci, 15 (2014), 19074-19091.
22 B. Ibrahim, R. Henze, G. Gruenert, M. Egbert, J. Huwald and P. Dittrich, Spatial rule-based modeling: A method and its application to the human mitotic kinetochore, Cells, 2 (2013), 506-544.
23 B. Ibrahim, E. Schmitt, P. Dittrich and S. Diekmann, In silico study of kinetochore control, amplification, and inhibition effects in MCC assembly, Bio Systems, 95 (2009), 35-50.
24 G. J. Kops, B. A. Weaver and D. W. Cleveland, On the road to cancer: Aneuploidy and the mitotic checkpoint, Nat Rev Cancer, 5 (2005), 773-785.
25 P. Kreyssig, G. Escuela, B. Reynaert, T. Veloz, B. Ibrahim and P. Dittrich, Cycles and the qualitative evolution of chemical systems, PLoS One, 7 (2012), e45772.
26 P. Kreyssig, C. Wozar, S. Peter, T. Veloz, B. Ibrahim and P. Dittrich, Effects of small particle numbers on long-term behaviour in discrete biochemical systems, Bioinformatics, 30 (2014), i475-i481.
27 M. Lohel, B. Ibrahim, S. Diekmann and P. Dittrich, The role of localization in the operation of the mitotic spindle assembly checkpoint, Cell Cycle, 8 (2009), 2650-2660.
28 S. Marques, J. Fonseca, P. MA Silva and H. Bousbaa, Targeting the spindle assembly checkpoint for breast cancer treatment, Curr Cancer Drug Targets, 15 (2015), 272-281.
29 H. B. Mistry, D. E. MacCallum, R. C. Jackson, M. A. J. Chaplain and F. A. Davidson, Modeling the temporal evolution of the spindle assembly checkpoint and role of Aurora B kinase, Proc Natl Acad Sci U S A, 105 (2008), 20215-20220.
30 A. Musacchio and E. D. Salmon, The spindle-assembly checkpoint in space and time, Nat Rev Mol Cell Biol, 8 (2007), 379-393.
31 C. L. Rieder, R. W. Cole, A. Khodjakov and G. Sluder, The checkpoint delaying anaphase in response to chromosome monoorientation is mediated by an inhibitory signal produced by unattached kinetochores, J Cell Biol, 130 (1995), 941-948.
32 C. L. Rieder, A. Schultz, R. Cole and G. Sluder, Anaphase onset in vertebrate somatic cells is controlled by a checkpoint that monitors sister kinetochore attachment to the spindle, J Cell Biol, 127 (1994), 1301-1310.
33 A. D. Rudner and A. W. Murray, The spindle assembly checkpoint, Curr Opin Cell Biol, 8 (1996), 773-780.
34 R. P. Sear and M. Howard, Modeling dual pathways for the metazoan spindle assembly checkpoint, Proc Natl Acad Sci U S A, 103 (2006), 16758-16763.
35 L. F. Shampine and M. W. Reichelt, The matlab ode suite, SIAM J Sci Comput, 18 (1997), 1-22.       
36 R. D. Skeel and M. Berzins, A method for the spatial discretization of parabolic equations in one space variable, SIAM J Sci Comput, 11 (1990), 1-32.       
37 F. Stegmeier, M. Rape, V. M. Draviam, G. Nalepa, M. E. Sowa, X. L. Ang, E. R. McDonald, M. Z. Li, G. J. Hannon, P. K. Sorger, M. W. Kirschner, J. W. Harper and S. J. Elledge, Anaphase initiation is regulated by antagonistic ubiquitination and deubiquitination activities, Nature, 446 (2007), 876-881.
38 S. Tschernyschkow, S. Herda, G. Gruenert, V. Döring, D. Görlich, A. Hofmeister, C. Hoischen, P. Dittrich, S. Diekmann and B. Ibrahim, Rule-based modeling and simulations of the inner kinetochore structure, Prog Biophys Mol Biol, 113 (2013), 33-45.
39 A. Verdugo, P. K. Vinod, J. J. Tyson and B. Novak, Molecular mechanisms creating bistable switches at cell cycle transitions, Open Biol, 3 (2013), 120179.
40 Z. Wang, J. V. Shah, M. W. Berns and D. W. Cleveland, In vivo quantitative studies of dynamic intracellular processes using fluorescence correlation spectroscopy, Biophys J, 91 (2006), 343-351.
41 T. Wilhelm, The smallest chemical reaction system with bistability, BMC Syst Biol, 3 (2009), p90.

Go to top