Question
vesaidles of the cardiac sarcoplasmic reticulum (CSR) are incubated with ATP. w' and Ca", they take up Ca" and reach a pseudo steady-state. This is a steady when state that changes, but slowly. The uptake of Ca2+ is mediated by the SERCAZa Ca- ATPase. The uptake reaction can be quenched by adding EGTA to the external solution, which binds the Ca 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* that was already taken up by the vesicles leaks out passively A The amount of Ca 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 Ca" uptake is 40 nmol mg'. In separate experiments, the enclosed volume of the CSR vesicles was determined to be 5 uL mg. What is the approximate concentration of Ca inside the vesicles at steady-state? The total Ca" concentration is its amount divided by the volume in which it is distributed. In this case the amount is 40 nmol mg CSR protein and the volume is 5 pl mg CSR protein. The concentration is estimated as (1 point) The average vesicle size determined by electron microscopy is abou is the volume and surface area of a vesicle this size, assuming it is a sphere? (1 point) t 150 nm. What B. 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? (1 point) D. The initial passive efflux at a load of 40 nmol mg! when the pump is stopped is 16 nmol min'mg". Convert this to a flux in units of nmol cm2s by dividing by the surface area per mg of CSR protein and converting min to s. (1 point) E. What is the passive permeability to Ca? in cm s'? (1 point)
Explanation / Answer
A. Approximate concentration of Calcium ions = amount of calcium ion taken up by vesicle/ volume in L
= 40 x 10-9 mol mg-1 / 5 x 10-6 L mg-1
= 8 x10-3 mol/L (also equivalent to 8000nmol/ cm3 ; 1L=1000cm3)
B. Size of the vesicle =150nm; therefore radius = 75nm
volume of the vesicles (vesicle being sphere) = 4/3*pi*r3
= 4/3 x 22/7 x (75 x 10-9)3
=1.77 x 10-21 m3 (equivalent to 1.77 x 10-18; 1m3 = 1000L)
surface area of the vesicle =4*pi*r2
= 4 X 22/7 x (75 x10-9) 2
= 7.068 x 10-14 m2 (equivalent to 7.06 x 10-10 cm2; 1m2 = 104 cm2
C. Number of vesicles per mg of CSR proteins
= enclosed volume of vesicle aggregates/ volume of each vesicle
= 5 x 10-6 L mg-1/ 1.77 x 10-18 L
= 2.82 x 1012 vesicles/ mg of CSR proteins
Total surface area available per mg of CSR proteins = No. of vesicles x Surface area of each vesicle
= 2.82 x 1012 x 7.06 x 10-10 cm2
=19.9 x 102 cm2 per mg of CSR proteins
D. Conversion of flux into nmol cm-2 sec-1 = initial passive flux/ Surface area per mg CSR protein
= 16 nmol mg-1/ (19.9 x102 cm2 x 60 s mg-1)
= 1.34 x 10-4 nmol cm-2 sec-1
E. Passive Permeability to Calcium ions in cm sec-1 = Total flux / Concentration of Calcium ion within vesicle
= 1.34 x 10-4 nmol cm-2 sec-1 / 8000nmol cm-3
=1.675 x 10-8 cm/sec
