Computing the Stochastic Dynamics of Phosphorylation Networks

被引:1
作者
Steijaert, M. N. [1 ]
Van den Brink, J. H. K. [1 ]
Liekens, A. M. L. [2 ]
Hilbers, P. A. J. [1 ]
Ten Eikelder, H. M. M. [1 ]
机构
[1] Eindhoven Univ Technol, Dept Biomed Engn, NL-5600 MB Eindhoven, Netherlands
[2] Univ Antwerp VIB, Dept Mol Genet, Antwerp, Belgium
关键词
biochemical networks; databases; functional genomics; genomics; literature data-mining; stochastic processes; PROTEIN REFERENCE DATABASE; CHEMICAL-KINETICS; SYSTEMS; UPDATE;
D O I
10.1089/cmb.2009.0059
中图分类号
Q5 [生物化学];
学科分类号
071010 ; 081704 ;
摘要
Cells of all organisms share the ability to respond to various extracellular signals. Depending on the cell type and the organism, these signals may include hormones secreted by other cells or changes in nutrient concentrations. The signals are processed by an intricate network of protein-protein interactions, including phosphorylation and de-phosphorylation events. As some signaling proteins are only present in low concentrations, random fluctuations may affect the dynamics of the network. The mathematical modeling of networks with significant random fluctuations requires the use of stochastic methods. The stochastic dynamics of a chemical reaction system are described by the Chemical Master Equation. Often the numerical evaluation of this equation is problematic. The first problem is that many systems have an infinite number of possible states; leaving simulations of individual trajectories as the only alternative. To circumvent this problem, we focus on a class of systems that have a finite state space. More specifically, we focus on networks of phosphorylation cycles without taking into account the synthesis and degradation of proteins. The second problem is that memory requirements cause a practical limit to the size of systems that can be evaluated. In this paper, we discuss how these limitations can be overcome using parallel computation and methods dealing efficiently with the available memory. These methods were implemented in a parallel C++ program. We discuss two networks for which the stochastic dynamics were evaluated using this program: a single phosphorylation cycle and an oscillating MAP-kinase cascade.
引用
收藏
页码:189 / 199
页数:11
相关论文
共 16 条
  • [2] Global analysis of protein expression in yeast
    Ghaemmaghami, S
    Huh, W
    Bower, K
    Howson, RW
    Belle, A
    Dephoure, N
    O'Shea, EK
    Weissman, JS
    [J]. NATURE, 2003, 425 (6959) : 737 - 741
  • [3] Stochastic simulation of chemical kinetics
    Gillespie, Daniel T.
    [J]. ANNUAL REVIEW OF PHYSICAL CHEMISTRY, 2007, 58 (35-55) : 35 - 55
  • [4] GENERAL METHOD FOR NUMERICALLY SIMULATING STOCHASTIC TIME EVOLUTION OF COUPLED CHEMICAL-REACTIONS
    GILLESPIE, DT
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1976, 22 (04) : 403 - 434
  • [5] AN AMPLIFIED SENSITIVITY ARISING FROM COVALENT MODIFICATION IN BIOLOGICAL-SYSTEMS
    GOLDBETER, A
    KOSHLAND, DE
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-BIOLOGICAL SCIENCES, 1981, 78 (11): : 6840 - 6844
  • [6] Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades
    Kholodenko, BN
    [J]. EUROPEAN JOURNAL OF BIOCHEMISTRY, 2000, 267 (06): : 1583 - 1588
  • [7] ESTIMATING THE LARGEST EIGENVALUE BY THE POWER AND LANCZOS ALGORITHMS WITH A RANDOM START
    KUCZYNSKI, J
    WOZNIAKOWSKI, H
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1992, 13 (04) : 1094 - 1122
  • [8] Proteomic analysis of post-translational modifications
    Mann, M
    Jensen, ON
    [J]. NATURE BIOTECHNOLOGY, 2003, 21 (03) : 255 - 261
  • [9] STOCHASTIC APPROACH TO CHEMICAL KINETICS
    MCQUARRI.DA
    [J]. JOURNAL OF APPLIED PROBABILITY, 1967, 4 (03) : 413 - +
  • [10] Human protein reference database - 2006 update
    Mishra, Gopa R.
    Suresh, M.
    Kumaran, K.
    Kannabiran, N.
    Suresh, Shubha
    Bala, P.
    Shivakumar, K.
    Anuradha, N.
    Reddy, Raghunath
    Raghavan, T. Madhan
    Menon, Shalini
    Hanumanthu, G.
    Gupta, Malvika
    Upendran, Sapna
    Gupta, Shweta
    Mahesh, M.
    Jacob, Bincy
    Mathew, Pinky
    Chatterjee, Pritam
    Arun, K. S.
    Sharma, Salil
    Chandrika, K. N.
    Deshpande, Nandan
    Palvankar, Kshitish
    Raghavnath, R.
    Krishnakanth, R.
    Karathia, Hiren
    Rekha, B.
    Nayak, Rashmi
    Vishnupriya, G.
    Kumar, H. G. Mohan
    Nagini, M.
    Kumar, G. S. Sameer
    Jose, Rojan
    Deepthi, P.
    Mohan, S. Sujatha
    Gandhi, T. K. B.
    Harsha, H. C.
    Deshpande, Krishna S.
    Sarker, Malabika
    Prasad, T. S. Keshava
    Pandey, Akhilesh
    [J]. NUCLEIC ACIDS RESEARCH, 2006, 34 : D411 - D414