bpc10_protein2b

bpc10_protein2b - Principles of protein-protein...

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Principles of protein-protein interactions Biophysical Chemistry 1, Fall 2010 Fundamentals of biological thermodynamics Basics of protein-protein recognition and interactions Reading assignment: Slater, Chap. 3 (handout)
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What does a force Feld look like? U = bonds K b ( b b eq ) 2 + angles K θ ( θ θ eq ) 2 + impropers K w w 2 + torsions K φ cos ( n φ )+ nonbonded pairs ° 4 ε ± ² σ r ³ 12 ² σ r ³ 6 ´ + q i q j r µ C O N H H H O H H 1 2 3 formamide water
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Lightening intro to biological thermdynamics A system is defned as the matter within a defned region oF space (i.e., reactants, products, solvent) The matter in the rest oF the universe is called the surroundings
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The frst law oF thermodynamics The total energy of a system and its surroundings is constant In any physical or chemical change, the total amount of energy in the universe remains constant, although the form of the energy may change .
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What is “U” (internal energy)? The internal energy of a system is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. U is a state function, that is, its value depends only on the current state of the system
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Energy is heat + work ! U = W + Q Work involves the non-random movement of particles Heat involves the random movement of particles
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Entropy and probability (qualitative!) p (H) = w exp(–H/RT)
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The Boltzmann entropy S = k ln N
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(good reading: J.C. Slater, “Introduction to Chemical Physics”; Dover, Chapter III) First law of thermodynamics: dU = dQ dW or U = ° dU = ° dQ ° dW (1) Second law of thermodynamics: dS dQ / T or TdS dU + dW (2)
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Connections to microscopic properties Let p i be the probability (fraction) of micro-state i . Then we can postulate a connection to the entropy: S = k i p i ln p i (3) This is large when the system is “random”. For example, if p i = 1 / W (same for all i ), then S = k ln W . This entropy is also additive (or “extensive”). Consider two uncorrelated systems that have a total number of states W 1 and W 2 . The total number of possibilities for the combined system is W 1 W 2 . Then: S = k ln ( W 1 W 2 )= k ln W 1 + k ln W 2 = S 1 + S 2 (4)
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The canonical ensemble: temperature Now consider dividing an isolated system (whose total energy U is therefore Fxed) into a number of subsystems, each of which could have its own internal energy E i , but where there is thermal contact between the subsystems, so that energy can be transferred among them. The Fxed total energy is U = i E i p i where p i is the probability that subsystem i will have energy E i . Let us Fnd the most
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This note was uploaded on 01/15/2012 for the course CHE 543 taught by Professor Staff during the Fall '10 term at Syracuse.

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bpc10_protein2b - Principles of protein-protein...

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