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

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

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

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

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

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

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

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

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

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

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Effects of Stochastic Fluctuations Master Equation: Exactly Solvable 3 species model: Generating function: Solution: [X]+[Z]=M=const Origin of Stochastic Bistability Z X rate 2 rate 1 Z d ~ 1/(k 3 n y ) f ~ 1/(k 2 n x n y n z ) ff dd P( ) (activation) (de-activation)

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Effects of Stochastic Fluctuations Master Equation: 3 species model: Generating function: Solution: ff dd P( ) ff dd reduction of n y and k 3 ff dd P( ) ff dd reduction of n y and k 3 discrete particle number stochastic fluctuations [X]+[Z]=M=const Scaling analysis (in the limit, ) k3k3 mean field scaling variable different from

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

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