Question

Barnase is a bacterial protein that is lethal to the cell unless it is expressed with its inhibitor barstar. Barstar must bind to barnase very quickly before barnase kills the cell that made it. Therefore, barnase and barstar use electrostatic attraction to find each other quickly (Schreiber and Fersht, 1996).

a) At neutral pH, barnase has a charge +1e and barstar has a charge −6e. Calculate the magnitude of the force between the two molecules if they are 8 nm (8 × 10−9 m) apart. Remember, the molecules will be in water, which has a dielectric constant κ = 80.

b) Consider the arrangement of charged molecules shown below. Draw a free body diagram showing the forces acting on the barnase. Which direction do you expect the net force will be?

c) Write each force on your free body diagram as x, y components. For example Fi = (Fix, Fiy), where i is an identifier for the object creating the force. Where appropriate, use Trig relationships to express these components in terms of the vector magnitude. Now add these vectors to find the total force in terms of these components.

d) Insert symbolic expressions for each component of the force. This expression should not have any numbers yet. This means that each distance and charge should have a unique identifier. Give each distance and charge a name and label it on a sketch of the system. e) Insert numbers and units to evaluate the x and y components of the total force.

Answer 1

Part a)

two charges :  

  

and the distance : d =

Force is given as:

Part b and c:

Here FB is the force due to Barstar and FA is the force due to ATP.

So the components of the forces are:

and

So the components of the net focrce are given as

or,

part d:

on putting the values :