signaling_equilibrium%20binding

signaling_equilibrium%20binding - Survival in changing...

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Survival in changing environments • Temperature •L igh t •Nu tr ien t •pH • Cell density •… cellular network Input Output •Gene expression •Enzymatic activity •Motility •…
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Example: Signaling in animals 1) (a-c) cell-to-cell signaling by extracellular chemicals that occur over distances from a few micrometers in autocrine and paracrine signaling to several meters in endocrine signaling. 2) Proteins attached to the plasma membrane of one cell can interact directly with receptors on an adjacent cell.
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II. Equilibrium binding Examples: Receptor / ligand binding (Very first step in cell signaling) • Binding of O 2 to hemoglobin • Binding of proteins to DNA • Binding of ions to polymer fibers
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1. The large molecule has only one binding site. P P + A + P k r k f PA A: small molecule, P: large molecule At equilibrium, k f [A][P] = k r [PA] ] P ][ A [ ] PA [ k k K r f = = or Define (number of bound molecule A per molecule P = average number of binding sites on P that are occupied by A) 0 bound ] P [ ] A [ = ν
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¾ ν depends on T, P, and [A]. ¾ The curve of ν versus [A] is called binding isotherm if T = const. For the reaction with only one binding site on P, ] PA [ ] P [ ] PA [ ] P [ ] A [ 0 bound + = = ν ] A [ K 1 ] A [ K ] P ][ A [ K ] P [ ] P ][ A [ K ] PA [ ] P [ ] PA [ + = + = + = ν At equilibrium, When ν = 0.5, [A] =1/ K.
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2. The large molecule P has N identical binding sites and they are independent of each other. Since these sites are independent , we can consider binding to each site as an independent reaction. For each reaction, we have: A + P i AP i , where P i indicates the concentration of the i th binding site. For each of these reaction, we have [AP i ] = K[A][P i ] 0 /(1 + K[A]), where [P i ] 0 = [P] 0 Thus the total bound A is: [A] bound = [AP i ] = NK[A][P i ] 0 /(1 + K[A]), v = [A] bound / [P] 0 = NK[A]/(1+ K[A]) A P K K K K
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Binding isotherm Initial slope = N K Approaches N v [A] Applies to equilibrium data
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] A [ 1 NK 1 N N = ν ν N 1 ] A [ 1 NK 1 1 + = ν ] A [ K 1 ] A [ NK + = ν ] A [ ) N ( K ν = ν (bound/free) ν/[Α] ν = ν K KN ] A [ slope = -K (Scatchard Eq) ν N (bound) (Scatchard Plot): applies to equilibrium
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Temporal evolution . Consider the limiting case where [A] 0 >> [P] 0 .
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signaling_equilibrium%20binding - Survival in changing...

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