Question

You discover a new mutation in amyloid beta protein that causes early onset of Alzheimers (mutation Pro-> Ala). This lowers the temp of unfolding from 50 degrees C to 40 degrees C and this loss in stability causes amyloid formation in vitro. The mutatuion occurs in a beta turn and does not effect enthalpic contributions to stability. Delta H of folding = -180kJ/mol. If the destabilizing contributions are only entropic, find delta S of folding for both the mutant and wildtype. Then find delta G of denaturation and the equilibrium constant of denaturation at 25 degrees C. Finally, assume that the native state of bot the wild type and the mutant have isoenergetic states of 1 and calculate the number of isoenergetic states in the completely denatured protein.

Answer 1

Answer:-

Delta H of folding= -180kJ/mol

temperature , T₁= 50 ^oC = 50+273= 323 K

T₂= 40^oC = 40+273 = 313 K

As given the mutant was at 50^oC , so

delta S of folding for mutant = - delta H of folding/T₁

= -(-180)/323

= 0.56 kJ/mol-K

= 560J/mol- K

delta S of folding for wildtype= - delta H of folding/T₂

= -(180)/313

= 0.58 kJ/mol-K

=580 J/mol-K

delta G of denaturation and Equilibrium constant at 25 ⁰C=(25+273=298)=T

delta G of denaturation = delta H of folding- T* delta S

= -180 - 298*(0.58-0.56))

= -180-5.96

= -185.96 kJ/mol

As we knowm that delta G = - RTlnK

lnK= - delta G/RT

lnK = -(-185.96)/8.314*298

lnK = 185.96*10³/2477.572

lnK = 75.057

K= exp(77.057))

K = 3.59*10³²