MIT20_441JF09_lec14_iy

MIT20_441JF09_lec14_iy - 2.79J/3.96J/20.441J/HST.552J...

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2.79J/3.96J/20.441J/HST.552J Biological Specificity and Cooperativity (From chance to necessity) 1. Adsorption of ligands on most biomaterials surfaces as a random process. Non- interacting sites. (a) Stochastic independence . Outcome of n th trial does not depend on outcome of ( n 1 ) st trial. If Prob. of event = () and Prob. of event B = () , then Prob. of event APA PB “first A and then B ” is PA B ( ) . B ( ) ( ) ( ) × PB if trials are stochastically independent. = PA (b) Independent trials . With two outcomes only: Bernoulli trials. pq 1. If += probabilities remain constant throughout trials, then for a given sequence of heads and tails : H T P HHTHT TTH ( ⋅⋅⋅ ) = ppqpq ⋅⋅ qqp . Stochastic independence of successive trials. Casino example: Does Nature have memory? (c) Random walks of different kinds: The 0.5-power rule. 1 1 1 Kinetic theory of gases: = ( kT / m ) υ 2 2 2 ; T 2 . 1 1 1 x 2 2 2 Diffusion: = ( 2 Dt ) 2 ; x T . 1 1 1 Unstretched macromolecule: r = ( ) r N 2 2 N l 2 2 ; 2 . Ligand adsorption onto n identical noninteracting sites of protein molecule: nk A [ ] v = moles bound ligand ÷ moles total protein = 1 + kA [] .
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2 2.79J/3.96J/20.441J/HST552J 2. Adsorption on interacting sites. (a) Loss of randomness during various physiochemical or biological processes. Compress a gas. Impose a concentration gradient. Stretch a macromolecule. Adsorb ligand onto protein. Interacting sites. nk A [ ] n v = moles bound ligand ÷ moles total protein = n . 1 + kA [] (b) Sigma-shaped curves. Oxygenation of hemoglobin. (c) Micelle formation. Cell membrane formation. (d) How large need n be to achieve cooperativity? Myoglobin vs. hemoglobin. 3. Cooperative processes. (a) Outcome of n th trial depends on outcome of ( n 1 ) st trial. (b) How to choose between a car and a goat. (c) Enzyme-substrate interaction. (d) ECM protein –cell receptor interaction. (e) Reversible melting of quaternary structure of collagen. (f) Simple one-dimensional statistical model of a critical transition as a cooperative process (See below #5). Nearest-neighbor interactions are sufficient for an “all or none” transition provided that the energy cost of the hybrid state is high enough and the sequence is long enough. The classical “lock-and-key” fit is not necessary. (g) A thermodynamic representation of a helix-coil transition: Gibbs free energy and the first-order transition. 4. The unit cell process: Inside and outside the control volume dV . (a) Regulators diffuse into and out of control volume dV . (b) Cell-matrix interaction inside dV is a cooperative process. Another way of putting it: the cell-matrix interaction is biologically specific. 2
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3 2.79J/3.96J/20.441J/HST552J 5. A model of a critical transition from noncooperative to cooperative cell behavior. What is cooperativity in cell biology? Cells cooperate, i.e., communicate with each other and acquire a common phenotype, following formation of condensed states of biological matter. States of this type comprise cells, usually embedded in matrix, that are arranged in close proximity with each other and frequently function as a single unit. Examples of
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MIT20_441JF09_lec14_iy - 2.79J/3.96J/20.441J/HST.552J...

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