1. Disc-shaped phospholipid particles, called bicelles, can be used to mimic mem
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1. Disc-shaped phospholipid particles, called bicelles, can be used to mimic membrane bilayers in order to study protein-membrane interactions in vitro. Bicelles are flattened micelles that look like a pancake (40 À thick; lipid bilayer is "36 A thick) bicelle 40 A a) If each methylene (-CHz-) group in a straight-chain hydrocarbon advances the chain length by about is this? (Note, you should consider the terminal carboxylic acid C as a methylene group.) (5 pts) 0.13 nm, what length fatty acid would most likely be found in each half of the bicelle? What fatty acid b) Would you come to the same conclusion for a typical plasma membrane? If not, which length fatty acid(s) would you likely find in a typical cellular membrane? Show calculations and explain. (3 pts)Explanation / Answer
In this pH range, the phosphate groups on all lipids in the bicelle are negatively charged. The charge will then depend on the ionization state of the amino group: the lipid molecule will be neutral when protonated, and will be negatively charged when it is deprotonated. In general, since at pKa half of the molecules are protonated ([A] = [HA]), the total charge of the bicelle at pH 9.0 should be negative and equal half of the number of molecules in the bicelle, i.e. (-1)*1000 /2 = -500. The pH7.0 case requires a somewhat more detailed calculation, so let’s first do it for a general case. Let NA ~ [A] be the amount of lipids in the bicelle that are deprotonated (hence have charge e – this amount we want to know) and NHA ~ [HA] is the amount that is protonated (i.e. neutral). The following equations then apply: NHA + NA = 1000, and NA/NHA = [A]/[HA] = l0pH-pKa. Expressing NHA (NHA = 1000 – NA) from the first and substituting it into the second equation then gives: NA/(1000 – NA) = l0pH-pKa. From here we have NA = 1000 / [1 + 10pKa - pH]. At pH = 9.0, NA = 1000/2 = 500 half molecules are protonated at pH = pKa and the charge is - 500. At pH = 7.0, NA = 1000/101 = 9.9 the net charge is –10..
The full answer is: 4.0 < pH < 6.0. The number of charged molecules per bicelle should be less than 1. For NA = 1, NHA = 999, and from Henderson-Hasselbalch equation: pH = pKa + log(NA/NHA) = 9.0 + log(1/999) = 6.0. Below pH6.0 all amino groups on the bicelle will be protonated. Lowering the pH further will eventually reach the point when the phosphate group on at least one molecule gets protonated: NA = 999, NHA = 1. This will happen (for phosphate group) at pH = pKa + log(999/1) = 4.0. c) (5 pts) List all interactions that you think are important for forming bicelles and for their stability in aqueous solution at neutral pH. Will raising the pH to 9.0 increase or decrease the stability of these particles, and how will this affect their shape? Explain your reasoning.
In this pH range, the phosphate groups on all lipids in the bicelle are negatively charged. The charge will then depend on the ionization state of the amino group: the lipid molecule will be neutral when protonated, and will be negatively charged when it is deprotonated. In general, since at pKa half of the molecules are protonated ([A] = [HA]), the total charge of the bicelle at pH 9.0 should be negative and equal half of the number of molecules in the bicelle, i.e. (-1)*1000 /2 = -500. The pH7.0 case requires a somewhat more detailed calculation, so let’s first do it for a general case. Let NA ~ [A] be the amount of lipids in the bicelle that are deprotonated (hence have charge e – this amount we want to know) and NHA ~ [HA] is the amount that is protonated (i.e. neutral). The following equations then apply: NHA + NA = 1000, and NA/NHA = [A]/[HA] = l0pH-pKa. Expressing NHA (NHA = 1000 – NA) from the first and substituting it into the second equation then gives: NA/(1000 – NA) = l0pH-pKa. From here we have NA = 1000 / [1 + 10pKa - pH]. At pH = 9.0, NA = 1000/2 = 500 half molecules are protonated at pH = pKa and the charge is - 500. At pH = 7.0, NA = 1000/101 = 9.9 the net charge is –10..
The full answer is: 4.0 < pH < 6.0. The number of charged molecules per bicelle should be less than 1. For NA = 1, NHA = 999, and from Henderson-Hasselbalch equation: pH = pKa + log(NA/NHA) = 9.0 + log(1/999) = 6.0. Below pH6.0 all amino groups on the bicelle will be protonated. Lowering the pH further will eventually reach the point when the phosphate group on at least one molecule gets protonated: NA = 999, NHA = 1. This will happen (for phosphate group) at pH = pKa + log(999/1) = 4.0. c)
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