The phospholipid molecule PIP2 (phosphatidylinositol 4,5-bisphosphate) is an imp

Question

The phospholipid molecule PIP2 (phosphatidylinositol 4,5-bisphosphate) is an important constituent of eukaryotic cell membranes. Its hydrophilic head group has a greater negative charge (typically -4e under physiological pH) than most of the other phospholipids present in eukaryotic cell membranes. PIP2 makes up only a small fraction of the membrane (typically ~1% by mole fraction), but in spite of this low concentration, it is known to form clusters with multiple PIP2 molecules that are thought to be important in cell signaling. It is an area of active research to understand the basis of this cluster formation.

Recent research* (Wang, Janmey, and coworkers) provides support for an electrostatic mechanism for this clustering, in which Ca2+ ions provide an attractive interaction holding together the PIP2 molecules. The detailed structure of how Ca2+ ions and PIP2 molecules are arranged in these clusters is not yet known. In this problem, we consider a highly simplified model simply to give a feel for how these interactions work.

A simplified model of such a cluster consists of five PIP2 molecules, each with a headgroup charge of –4e, and four Ca2+ ions. They are all placed on a grid where each grid square has sides of length s, as shown in the figure at the right.

In this problem we will explore whether the electric forces on the PIP2 ions in this model cluster tends to pull it together or blow it apart. In particular, we will focus on the uppermost PIP ion (labeled "0"), and determine whether it is being pulled into the molecule, thus providing needed stability, or being pushed away. We will treat each ion as a point charge.

Compute the electric force on the uppermost ion, due to each other ion, or pair of ions, as described below. Enter a positive number if the electric force is up, and enter a negative number if the electric force is down. Each answer should be a multiple of F0 (the force that an electron exerts on another electron a distance saway). For example, if the force is 2F0 pointing up, then you should enter "2".

Electric force due to ion #1:

Electric force due to ion #2:

Electric force due to ion #3:

Electric force due to ion #4:

Net electric force due to ions A and D:

Net electric force due to ions B and C:

NOTE: You should do the first "PIP2 cluster stability" question and answer it correctly before attempting this question.

Explanation / Answer

**Although it's more of a physics problem, still I can try.....

According to coulomb's law:

electric force due to ion#1 = kq1q2/s2; where q1= charge on point charge 1= -4e

and q2= charge exerted on 1 due to 0= +2e ; electric force on ion 1 due to 0= -16ke =lectric force on 1 due to 2 = lectric force on 1 due to 3

total lectric force on 1 due to PIP2 = -24ke (negative force implies an attractive force)

lectric force on 1 due to C (calcium) = +8ke/2 = 4ke= lectric force on 1 due be B

Under all cases , the overall attractive force is higher than the repulsive force.

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