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

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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

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Protein Sequestration Per BMAL Activate transcription PER BMAL translation Inactive Complex

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

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

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

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Kim and Forger result

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Trends in Amplitude vs Stoichiometry Goodwin PNF Implicit Sequestration

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

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

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

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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

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Stoichiometry Ueda Direct Hill RepressionUeda Implicit Sequestration

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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

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

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