Isolated cardiac sarcoplasmic reticulum vesicles have an average outside diamete

Question

Isolated cardiac sarcoplasmic reticulum vesicles have an average outside diameter of about 150 nm. The membrane itself is about 10nm thick. The enclosed volume can be estimated by measuring the efflux of passively loaded tracer materials such as mannitol, and the result gives 5 mu L per mg SR protein. A. How many vesicles are there per mg of SR protein? B. What is the surface area of the vesicles per mg of SR protein? C. If the SR Ca middot ATP ase ca^2+ uptake activity is 4 mu mol min^-1 mg^-1, what is the uptake activity per unit surface area?

Explanation / Answer

8A

We know that 1 liter = 1000 cm3

1 uL = 10-6 L

Therefore 1 uL = 1000 ×10-6 cm3

1cm equals to 107 nm

Therefore, 1 uL = 1000 ×10-6 (107)3 nm3

1 uL = 1000 ×10-6 ×1021 nm3

1 uL = 1000 ×1015 nm3

The enclosed volume of SR protein is given that is = 5uL per mg

Or, 5uL = 5×1000 ×1015 nm3 per mg

5uL = 5×1018 nm3 per mg

Now calculate vesicle’s volume

Vesicle’s outside diameter = 150nm

Thickness = 10nm

Therefore,

Vesicle’s inside diameter = Vesicle’s outside diameter - Thickness

Vesicle’s inside diameter = 150 -10 =140nm

Now the volume of vesicle = 4/3 r3

Here the r is the radius of the vesicle

Radius = diameter/2

Radius = 140/2 = 70nm

Now the volume is =4/3 ×3.14 × (70)3

= 1.3× 3.14 ×343000

= 1400126

Or, 14 × 105 nm3

Now to calculate number of vesicles we use the formula-

Volume of SR protein / Volume of a vesicle

= 5×1018 / 14 × 105

= 0.35 × 1013

= 35 × 1011 vesicles.

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