Question

4. Inspired by the natural design of cell membranes, you have invented a strange new semi-permeable membrane consisting of a water-impemeable base layer interspersed with hydrophilic transmembrane glycoproteins which form three types of channels. Channel type 'A' is approx imately 3 angstroms in diameter and lined with negative charges Channel type 'B' is approximately 3 angstroms in diameter also but lined with positive charges Channel type C is approximately 4 angstroms in diameter and electrically neutral This membrane separates two ionic solutions containing lithium (Li+) and potassium (K+) ions, as well as some impermeable anions (A, having the following concen trations. SOLAL 30 mM 170 mM 200 mM SOL#2 120 mM 80 mM 200 mM Li+ A- Assume solution 1 as your "reference" solution. This is analogous to the extracellular solution when analyzing neuronal membranes A. (Note:BecauseI did not cover this in class on Thursday, question 44 is not required -please do complete 4 B-E, however. I will discuss channel specificity briefly on Tuesday, and will post the solution to this along with the rest of the homework set. But... why not read the text and take a shot at answering it?!) Speculate on the specificity of the three channel types. Which channels would you expect to be Li+ and K+ channels and why? (Hint: compare the location of Li on the periodic table with K and Na, and think in terms of the relative degree of interaction that you might expect between the Li ion and surrounding water molecules, as compared to the ions you know something about). B. Assuming that this membrane is permeable to only Li+, what electric potential would you measure across the cell membrane (assume solution #1 is the reference or ground)? C. What would the potential be if the membrane was permeable to only K+2 D. What would the membrane potential be if the membrane permeability to Li+ was 15% that of the permeability to K+ E You discover that the Li+ penmeability is daylight-sensitive, increasing linearly from its rest value of 15% that of K+ at 6 AM daylight to a peak of 8-times that of K+ at high noon. You there fore place your membrane in the kitchen window to use as a "sundial" This morning when you woke up, you noticed that the sun shining in through the window created a -20 mV potential across your membrane. At that moment you knew that you were late for that nasty 8 oclock cass. Exactly how late were you? (Note: Do not make the mistake of assuming that a linear change in pemeability translates to a linear change in membrane potential most systems in nature are non-linear, inc luding this one!)

Answer 1

A)The atomic number of Li is 3 and that of K+ is 19.So size of potassium is more than Li because of the presence of two additional shells.

Due to the smaller size of Li+ ion ; the positive charge is more concentrated.So the the attraction between the lithium ion and water molecules is more than that with potassium.So the size of hydrated Li+ is more than that of hydrated K+.

Hence channel C(being larger) is Li+ channel and channnel A is K+ channel.

B)Potential = 61/z log (outside concentration/Inside comcentration)

= 61/1 log (30/120) = -61 log 4 = -36.73 mV

C)Potential = 61/1 log (170/80) =19.97 mV

D)The permeabilty of Lithium is 0.15 times that of potassium.

Potential = 61/1 log ( [ 0.15 *30 + 1* 170]/ 0.15*120+1*80)

= 61 log (174.5/98) =15.28 mV