Question

When vesicles of the cardiac sarcoplasmic reticulum (CSR) are incubated with ATP Mg^2+ and Ca^2+, they take up Ca^2+ and reach a pseudo steady-state. This is a steady state that changes, but slowly. The uptake of Ca2+ is mediated by the SERCA2a Ca-ATPase. The uptake reaction can be quenched by adding EGTA to the external solution, which binds the Ca^2+ outside of the vesicles, or by adding glucose plus hexokinase, that converts the ATP to ADP and glucose-6 phosphate. When the uptake reaction is stopped, Ca^2+ that was already taken up by the vesicles leaks out passively A. The amount of Ca^2+ taken up by the vesicles is generally normalized to the amount of CSR protein in mg rather than being expressed as a concentration. A typical steady state Ca2 uptake is 40 nmol mg^-1. In separate experiments, the enclosed volume of the CSR vesicles was determined to be 5 mu L mg. What is the approximate concentration of Ca^2+ inside the vesicles at steady-state? The total Ca^2+ concentration is its amount divided by the volume in which it is distributed. In this case the amount is 40 nmal mg CSR protein^-1 and the volume is 5 mu L mg CSR protein^-1, The concentration is estimated as B. The average vesicle size determined by electron microscopy is about 150 nm. What is the volume and surface area of a vesicle this size, assuming it is a sphere? C. Given that the enclosed volume of the aggregate vesicles is 5 iL mg-1, how many vesicles are there per mg of CSR protein? How much surface area is there per mg of CSR protein? D. The initial passive efflux at a load of 40 nmol mg when the pump is stopped is 16 nmol min^-1mg^-1. Convert this to a flux in units of nmol cm^-2 s^-1 by dividing by the surface area per mg of CSR protein and converting min to s. E. What is the passive permeability to Ca^2+ in cm s^-1?

Answer 1

Answer

I added 4 and 5 as an attachment due to time constraint.

Explanation:

1. at a steady state ca2+ taken by vesicle = 40n/mol

enclosed volume of CSR = 5μ/mg

concentration of ca2+ in vesicle =

40*10⁻⁶/5x10⁻⁶

= 0.008

= 8x10⁻⁹mol/L

2. radius of circle =75nM

volume = 150nm

volume of vesicle = 4/3 x pi x r³

= 1.33 x 3.14 x (75x10⁻⁹)³

= 1.77 x 10⁻²¹

when we convert this we get

1.77x10⁻¹⁸L since 1m³ is equal to 100oL

surface area =4x3.14x(75x10⁻⁹)²

= 12.56x5.625⁻¹⁵

= 7.065x10⁻¹⁴m²

this is 7.065x10⁻¹⁰cm²

3. number of vesicle/CSR

= 5x10⁻⁶/1.77x10⁻¹⁸

= 2.824x10¹²

surface are = 2.824x10¹² x7.06x10⁻¹⁰

= 19.95x10²