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Agonists and Antagonists

APC. antagonist peptide. agonist peptide. T cell. stimulation suppressed. stimulation. Agonists and Antagonists. APC. agonist peptide. T cell. stimulation suppressed. stimulation. Agonists and Antagonists. Dueling positive and negative feedbacks. APC. agonist peptide.

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Agonists and Antagonists

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  1. APC antagonist peptide agonist peptide T cell stimulation suppressed stimulation Agonists and Antagonists APC agonist peptide T cell

  2. stimulation suppressed stimulation Agonists and Antagonists Dueling positive and negative feedbacks APC agonist peptide agonist peptide T cell

  3. Agonists and Antagonists Dueling positive and negative feedbacks APC APC Agonist concentration agonist peptide T cell activation (concentration of pErk) Scaling ? T cell Antagonist concentration D. Wylie, JD, A. K. Chakraborty, PNAS (2007) stimulation suppressed stimulation M. Artomov, JD, M Kardar, A. K. Chakraborty, PNAS (2007)

  4. +ve -ve Minimal Model 3 species model: [X]+[Z]=M=const • Irreversibility • Branching • Feedback with distinct • time scale Minimal Model for cell signaling with positive and negative feedbacks

  5. +ve -ve Minimal Model Mean field Analysis 3 species model: • Irreversibility • Branching • Feedback with distinct • time scale Rate equations : [X]+[Z]=M=const number conservation : initial values (t=0) : Minimal Model for cell signaling with positive and negative feedbacks

  6. +ve -ve Minimal Model Mean field Analysis 3 species model: • Irreversibility • Branching • Feedback with distinct • time scale Solutions: [X]+[Z]=M=const stability: no un-stable mode Minimal Model for cell signaling with positive and negative feedbacks

  7. +ve -ve Minimal Model Mean field Analysis 3 species model: • Irreversibility • Branching • Feedback with distinct • time scale [X]+[Z]=M=const Mean field Scaling: Minimal Model for cell signaling with positive and negative feedbacks

  8. +ve -ve Minimal Model Stochastic Fluctuations 3 species model: • Irreversibility • Branching • Feedback with distinct • time scale Master Equation: Gain-Loss equation for probabilities of states n For a simple reaction: [X]+[Z]=M=const thus, Minimal Model for cell signaling with positive and negative feedbacks

  9. Master Equation: Generating function: Solution: Effects of Stochastic Fluctuations 3 species model: Exactly Solvable

  10. large N large k3 Fixed k3/N purely stochastic origin of bimodality Effects of Stochastic Fluctuations 3 species model: Exactly Solvable Stochastic Analysis Mean field Master Equation: small N small k3 Fixed k3/N [X]+[Z]=M=const Generating function: Solution:

  11. X f ~ 1/(k2nxnynz) rate 1 P() Z rate 2 d ~ 1/(k3ny) Z d f Effects of Stochastic Fluctuations 3 species model: Exactly Solvable Origin of Stochastic Bistability (activation) Master Equation: [X]+[Z]=M=const (de-activation) Generating function: Solution:

  12. P() d f reduction of ny and k3 2 1.75 reaction rates 1.5 1.25 1 0.75 0.5 0.25 2 4 6 8 10 time, arbitrary units Effects of Stochastic Fluctuations 3 species model: Scaling analysis (in the limit, ) P() Master Equation: [X]+[Z]=M=const d f stochastic fluctuations k3 reduction of ny and k3 discrete particle number Generating function: different from Solution: mean field scaling variable P() P() d d f f

  13. agonist antagonist No signal Signaling product Cell Decision Mediated by Stochastic Fluctuations M. Artyomov, JD, M. Kardar, A. Chakraborty PNAS (2007)

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