Roles of Protein Ubiquitination and Degradation Kinetics in Biological Oscillations

Protein ubiquitination and degradation play important roles in many biological functions and are associated with many human diseases. It is well known that for biochemical oscillations to occur, proper degradation rates of the participating proteins are needed. In most mathematical models of biochemical reactions, linear degradation kinetics has been used. However, the degradation kinetics in real systems may be nonlinear, and how nonlinear degradation kinetics affects biological oscillations are not well understood. In this study, we first develop a biochemical reaction model of protein ubiquitination and degradation and calculate the degradation rate against the concentration of the free substrate. We show that the protein degradation kinetics mainly follows the Michaelis-Menten formulation with a time delay caused by ubiquitination and deubiquitination. We then study analytically how the Michaelis-Menten degradation kinetics affects the instabilities that lead to oscillations using three generic oscillation models: 1) a positive feedback mediated oscillator; 2) a positive-plus-negative feedback mediated oscillator; and 3) a negative feedback mediated oscillator. In all three cases, nonlinear degradation kinetics promotes oscillations, especially for the negative feedback mediated oscillator, resulting in much larger oscillation amplitudes and slower frequencies than those observed with linear kinetics. However, the time delay due to protein ubiquitination and deubiquitination generally suppresses oscillations, reducing the amplitude and increasing the frequency of the oscillations. These theoretical analyses provide mechanistic insights into the effects of specific proteins in the ubiquitination-proteasome system on biological oscillations.

[1]  Alan Garfinkel,et al.  Multi-scale modeling in biology: how to bridge the gaps between scales? , 2011, Progress in biophysics and molecular biology.

[2]  Vishva M. Dixit,et al.  Ubiquitylation in apoptosis: a post-translational modification at the edge of life and death , 2011, Nature Reviews Molecular Cell Biology.

[3]  Jin Wang,et al.  Quantifying the Waddington landscape and biological paths for development and differentiation , 2011, Proceedings of the National Academy of Sciences.

[4]  J. Tyson,et al.  Computational Cell Biology , 2010 .

[5]  M. Eilers,et al.  Ubiquitylation of the amino terminus of Myc by SCFβ-TrCP antagonizes SCFFbw7-mediated turnover , 2010, Nature Cell Biology.

[6]  Juliane Liepe,et al.  The 20S Proteasome Splicing Activity Discovered by SpliceMet , 2010, PLoS Comput. Biol..

[7]  L. Komuves,et al.  Ubiquitin hydrolase Dub3 promotes oncogenic transformation by stabilizing Cdc25A , 2010, Nature Cell Biology.

[8]  Albert Goldbeter,et al.  Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  R. Deshaies,et al.  Detection of Sequential Polyubiquitylation on a Millisecond Time-Scale , 2009, Nature.

[10]  K. Kaneko,et al.  The combination of positive and negative feedback loops confers exquisite flexibility to biochemical switches , 2009, Physical biology.

[11]  T. Vondriska,et al.  The effects of cascade length, kinetics and feedback loops on biological signal transduction dynamics in a simplified cascade model , 2009, Physical biology.

[12]  M. Petroski,et al.  The ubiquitin system, disease, and drug discovery , 2008, BMC Biochemistry.

[13]  Benjamin L Turner,et al.  Supporting Online Material Materials and Methods Som Text Figs. S1 to S3 Table S1 References Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops , 2022 .

[14]  Alexey Zaikin,et al.  Towards quantitative prediction of proteasomal digestion patterns of proteins , 2008, 0806.2594.

[15]  Wilson W Wong,et al.  Single-cell zeroth-order protein degradation enhances the robustness of synthetic oscillator , 2007, Molecular systems biology.

[16]  M. Pagano,et al.  The After-Hours Mutant Reveals a Role for Fbxl3 in Determining Mammalian Circadian Period , 2007, Science.

[17]  Michele Pagano,et al.  SCFFbxl3 Controls the Oscillation of the Circadian Clock by Directing the Degradation of Cryptochrome Proteins , 2007, Science.

[18]  K. Sneppen,et al.  Minimal model of spiky oscillations in NF-κB signaling , 2006 .

[19]  Nicolas E. Buchler,et al.  Nonlinear protein degradation and the function of genetic circuits. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Robert T Sauer,et al.  SspB delivery of substrates for ClpXP proteolysis probed by the design of improved degradation tags. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Zhilin Qu,et al.  Multisite phosphorylation and network dynamics of cyclin-dependent kinase signaling in the eukaryotic cell cycle. , 2004, Biophysical journal.

[22]  James R. Knight,et al.  A Protein Interaction Map of Drosophila melanogaster , 2003, Science.

[23]  J. Weiss,et al.  Dynamics of the cell cycle: checkpoints, sizers, and timers. , 2003, Biophysical journal.

[24]  J. Ferrell,et al.  A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision , 2003, Nature.

[25]  Anders Lansner,et al.  A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell. , 2003, Biophysical journal.

[26]  A. Goldbeter,et al.  Toward a detailed computational model for the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[28]  Eduardo Sontag,et al.  Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2 , 2003, Nature Cell Biology.

[29]  Zhilin Qu,et al.  Regulation of the mammalian cell cycle: a model of the G1-to-S transition. , 2003, American journal of physiology. Cell physiology.

[30]  John J. Tyson,et al.  Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[31]  Prahlad T. Ram,et al.  MAP Kinase Phosphatase As a Locus of Flexibility in a Mitogen-Activated Protein Kinase Signaling Network , 2002, Science.

[32]  A. Ciechanover,et al.  The ubiquitin-proteasome proteolytic pathway: destruction for the sake of construction. , 2002, Physiological reviews.

[33]  P. O’Farrell,et al.  The schedule of destruction of three mitotic cyclins can dictate the timing of events during exit from mitosis , 2001, Current Biology.

[34]  M. Kitagawa,et al.  Targeted disruption of Skp2 results in accumulation of cyclin E and p27Kip1, polyploidy and centrosome overduplication , 2000, The EMBO journal.

[35]  B. Kholodenko,et al.  Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. , 2000, European journal of biochemistry.

[36]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[37]  Yi-Song Wang,et al.  Deletion of the Cul1 gene in mice causes arrest in early embryogenesis and accumulation of cyclin E , 1999, Current Biology.

[38]  A. Murray,et al.  Budding yeast Cdc20: a target of the spindle checkpoint. , 1998, Science.

[39]  Julio M. Ottino,et al.  Nonlinear dynamics and chaos (with applications to Physics; Biology; Chemistry; and engineering). By S. H. Strogatz; addison‐wesley; reading; MA; 1994; 498 pp.; $51.95 (hard cover) , 1995 .

[40]  David O. Morgan,et al.  Principles of CDK regulation , 1995, Nature.

[41]  A Goldbeter,et al.  A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[42]  J. Tyson.  Modeling the cell division cycle: cdc2 and cyclin interactions. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[43]  Lansun Ohen,et al.  A BIOCHEMICAL OSCILLATION , 1985 .

[44]  D. Koshland,et al.  Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects. , 1984, The Journal of biological chemistry.

[45]  R. D. Bliss,et al.  Role of feedback inhibition in stabilizing the classical operon. , 1982, Journal of theoretical biology.

[46]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[47]  P. Maini,et al.  Multiscale modeling in biology , 2007 .

[48]  James E. Ferrell,et al.  A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision , 2007, Nature.

[49]  Kim Sneppen,et al.  Minimal model of spiky oscillations in NF-kappaB signaling. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[50]  John J. Tyson,et al.  Biochemical Oscillations , 2004 .

[51]  Huxley Af,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve. 1952. , 1990 .

[52]  J. Griffith,et al.  Mathematics of cellular control processes. I. Negative feedback to one gene. , 1968, Journal of theoretical biology.

[53]  B. Goodwin.  Oscillatory behavior in enzymatic control processes. , 1965, Advances in enzyme regulation.

[54]  A. U.S.  Ultrasensitivity in Biochemical Systems Controlled by Covalent Modification , 2022 .

[55]  E. Wimmer,et al.  MAP Kinase Phosphatase As a Locus of Flexibility in a Mitogen-Activated Protein Kinase Signaling Network , 2022 .