# The Importance of Activator- Repressor Balance in Various Models of Sequestration for Circadian Clocks Roxana Gheorghe ‘15 Mary Fletcher ‘13 Olivia Lang.

## Presentation on theme: "The Importance of Activator- Repressor Balance in Various Models of Sequestration for Circadian Clocks Roxana Gheorghe ‘15 Mary Fletcher ‘13 Olivia Lang."— Presentation transcript:

The Importance of Activator- Repressor Balance in Various Models of Sequestration for Circadian Clocks Roxana Gheorghe ‘15 Mary Fletcher ‘13 Olivia Lang ‘15

Circadian Clock Model Per PER BMAL Activate Repress dPer/dt = f 1 (Per, PER, BMAL) dPER/dt = f 2 (Per, PER, BMAL) dBMAL/dt = f 3 (Per, PER, BMAL) … transcription translation

Protein Sequestration Per BMAL Activate transcription PER BMAL translation Inactive Complex

Different Mathematical Models Explicit Implicit Direct Hill or Transcription Rate Expressions *J Kim, MSB 2012 *

Evaluating Models  Balanced Proteins -> High Oscillations -Kim and Forger BMAL PER

Finding Stoichiometry and Amplitude of a Set of Rate Constants A =.5289 S =.1681.1478

Kim and Forger result

Trends in Amplitude vs Stoichiometry Goodwin PNF Implicit Sequestration

Models Modeled after Repression Model Number of States Leloup & Goldbeter 2003 MammalianExplicit sequestration 16 Mirsky 2009MouseDirect Hill (1)21 Ueda 2000DrosophilaDirect Hill (2)10

Trends in Amplitude vs Stoichiometry Leloup & Goldbeter Ued a Mirsky Direct Hill Repression Implicit Sequestration Explicit Sequestration Average Stoichiometry Amplitude of Per mRNA

What’s Wrong?  Bad measure of stoichiometry  Maybe it’s not a sequestration modeling problem

Stoichiometry dPer/dt = f 1 (Per, PER, BMAL) = 0 dPER/dt = f 2 (Per, PER, BMAL) = 0 dBMAL/dt = f 3 (Per, PER, BMAL) = 0 … Per PER BMAL Activate Repress Transcription Translation PER fixed BMAL fixed Solve for Per fixed, PER fixed, BMAL fixed PER avg BMAL avg.1681.1478

Stoichiometry Ueda Direct Hill RepressionUeda Implicit Sequestration

Conclusion  The model of repression on its own does not appear to have a clear effect on the simulation  Ratio at the fixed point is not always well approximated by the ratio of average concentrations

Acknowledgements  Thanks to Stephanie Taylor for mentoring us  We also thank the rest of the class for their helpful input

Download ppt "The Importance of Activator- Repressor Balance in Various Models of Sequestration for Circadian Clocks Roxana Gheorghe ‘15 Mary Fletcher ‘13 Olivia Lang."

Similar presentations