BMB170a_2011_PS2_key

# BMB170a_2011_PS2_key - BMB170A 2010 Problem Set 2 Proteins...

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1 BMB170A 2010 Problem Set 2: Proteins II KEY 1. Protein Folding (30 points total) a. Levinthal’s Paradox (10 points): Calculate the time it would take for a typical 300 residue protein to sample all conformations available to it if: - The Φ and Ψ angles can only adopt two stable conformations each (a gross underestimate) - Each sidechain samples two χ 1 angles with no other adjustments (another gross underestimate). Assume all sidechains have identities where two χ 1 angles are possible. - Singles bonds are estimated to reorient to different conformations 10 13 times per second Compare this value to the age of the universe (13.75 ± 0.17 billion years) and to the actual amount of time proteins typically take to fold (10 -6 to 10 2 seconds). What does this tell us about how proteins fold? Number of Possibilities: There are only 299 Φ and Ψ angles since the N and C termini do not have Φ and Ψ angles respectively. 300 299 299 2 2 2 = = = sidechain ψ φ Folding Time: seconds 926 556 31 = year 1 10 69 . 6 11 . 2 * . 2 * 2 2 * 2 * 2 _ _ _ 249 257 13 270 13 898 1 13 300 299 299 years x s x s x s s time sampling ons conformati of number t = = = = = = This number is considerably larger than the age of the universe and mindboggling larger than the amount of time it takes for a typical protein to fold (10 -6 to 10 2 seconds). Proteins obviously do not fold by random sampling of conformations. b. Inclusion Bodies (5 points): The following image is an electron micrograph of Escherichia coli cells taken by Scott Betts, formerly of the King Lab at MIT. The image clearly shows dark staining areas called inclusion bodies. Though the exact mechanism of their formation currently escapes explanation, these structures are seen as “graveyards” for unfolded or misfolded proteins and aggregates like discarded viral capsids and amyloids. Give three reasons why overexpression of an engineered protein in a foreign host might lead to the formation of inclusion bodies.

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2 Possible Answers: - Engineered proteins may be less stable and susceptible to unfolding due to destabilizing mutations. - Overexpression of a protein may supersaturate the cellular solution causing proteins to precipitate and unfold. - The cellular environment of the host may not match that of the original organism. The pH may differ or the organism may lack or posses post translational processing (glycosylations, non-canonical amino acids, disulfide bonds, chaperones) machinery that causes improper folding. c. Knots (5 points): Protein backbones exhibit a strong tendency against knots with only a handful showing knotted topologies (see http://knots.mit.edu/cgi-bin/knots/knotsubmit.pl?showlist=1& ). Why is this surprising with regard to entropy? Provide a possible explanation for why knotted topologies are more rare than expected.
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BMB170a_2011_PS2_key - BMB170A 2010 Problem Set 2 Proteins...

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