DG of unfolding of monomers by urea

1

• DG of unfolding of monomers by urea
• DG of dissociation/unfolding of dimers by GnHCl
• Denaturation examples of asparaginase.

2

• DG of denaturation of cytochrome c by urea
• Biochemistry, 2003, 42, 14606-13,
  Chattopadyay et al.
• In many stability analyses people are looking for
  folding intermediates or other partially stable
  states.
• Here the authors detect two folding intermediates
  of cytochrome c, when the protein is treated with
  SDS (sodium dodecylsulfate).
• In the simple case of urea as denaturant no
  folding intermediates of cytochrome c were
  detected.

3

• DG of denaturation of cytochrome c by urea

with urea
4

• Goal DG of denaturation
• Measurements and prediction ellipticity
  dependent on the concentration of urea
  (denaturant)
• Assumption The denaturation/renaturation step is
  is reversible. DGD depends linearly on urea.
• Unknown parameters ellipticity of the native and
  denatured state, half point of denaturation,
  cooperativity steepness of denaturation curve

5

• Equations
• Two state equilibrium
• c concentration of urea
• Conservation of mass
• Ellipticity is additive

(1)
(2)
(3)
6

• Equations
• Concentration of the denatured species (eliminate
  nat from (1) and (2)
• Ellipticity is proportional to the concentration

(4)
(5a)
(5b)
7

• Ellipticity as function of the denaturant
  concentration
• (5) and (2) in (3)
• (4) in (6)

(6)


(7)
(8)
Qnat, Qden ellipticity if all protein is native
/ denatured
8

• We still need to get DG information from the fits
  above.
• Equations DG is linearly dependent on urea
• with

(9)

(10)
9

• Write Kd as function of c

(11)

10

11

• The midpoint of transition can be reproduced well
  (fit 7,1 M, reported 7,2 M).
• DG(H2O) is fitted to 50 kJ/mol, but reported as
  34 kJ/mol.

12

• DG of dissociation/unfolding of dimers by GnHCl
• Biochemistry, 2003, 42, 14831-7, Moreau et
  al.
• Here, denaturation of a dimer, triosephosphate
  isomerase, is analyzed. Since the association
  reaction is bimolecular, the equilibrium is
  concentration dependent. Nevertheless, the
  observed dependence deviates from the expected
  dependence. Supported by further experiments,
  this can be explained by two very slowly
  interconverting native states.

13

• The denaturation curve has to be predicted
  theoretically in order to observe deviations from
  the simple two state model.
• Questions What is the function for the
  dissociated fraction a?
• How does this curve depend on protein?

14
0.12 mM TIM
1.2 mM TIM
15

• Goal DG of denaturation, dependence on protein
  concentration
• Measurements fluorescence (spectra) at different
  concentrations of GdnHCl (denaturant) and two
  protein concentrations
• Graph Fraction a of denatured protein as
  function of GdnHCl . This is calculated from the
  position of the emission maxima.
• Assumption emission peak position behaves as a
  weighted average

16

• Prediction a as function of GdnHCl .
• Assumption The denaturation/renaturation step is
  reversible, DG is linearly dependent on GdnHCl
  concentration
• Unknown parameters relative fluorescence
  intensity of the native and denatured state, half
  point of denaturation, cooperativity

17

• The calculation is done in two steps.
• First the fraction a(c) of denatured protein is
  calculated from experimental data.
• Second, a(c) is used to obtain DG.

18

• The observed parameter for denaturation is the
  wavelength lG (dependent on GdnHCl) of the
  fluorescence emission peak.
• For symmetrical peaks lG is the peak maximum.
• For complicated peaks an intensity-weighted
  emission maximum is used for lG

Il
l
19

• Determination of a
• If fraction a of the protein is denatured
  (unfolded), the two emission peaks of the native
  and denatured protein overlay. The observed
  wavelength lG of the emission peak is the
  weighted average of the native and denatured
  peaks (lN and lU).

lU
lG
lN
20

• In the first example the maximum is shifted a
  bit, but in the second, what is the observed
  maximum?

21

• The observed wavelength (lav) can be calculated
  as weighted average from the fraction a, lN, and
  lU.

(1)
I total intensity of a peak f fraction of
native/denatured protein
22

• The fraction f of native and denatured protein
  can be expressed in as
• Use these fs ((2) in (1))
• And resolve a

(2)


(3)
(4)
23

• The experimental data can now be used to
  calculate the as for the following graph

24

• Now, we need to find the equation how a depends
  on c, the GdnHCl concentration.
• Definition of a
• NB some authors also use a as the fraction of
  native protein.
• The following equations differ, whether the
  native state is a monomer or dimer (or ...)

25

• Monomers Dimers

26

• Monomers Dimers
• An important difference is, that the stability
  (DG) is independent of the protein concentration
  (tot) for monomers, but dependent for dimers!
• The reason is clear dilute dimers can dissociate
  and unfold more easily.

27

• Monomers
• A similar equation is used for dimers, but c0 and
  f are more complicated.

28

• How does the protein concentration influence the
  curves?
• The effect is most easily calculated for the
  midpoint of denaturation

29

• The calculated shift of c1/2 is 0.19 M, but only
  a shift of 0.08 M is observed

30

• Result One of the assumptions must be wrong.
• Further experiments show, that there are (at
  least) two native states, that interconvert very
  slowly. These two states show different
  denaturation behavior. In samples treated with
  0.6 M GdnHCl these two states can be separated on
  a gel filtration column. They show different
  denaturation kinetics. Nevertheless, they have
  identical covalent structures. Hence, they are
  stable discernable conformers.

31

• Notes on additional aspects of denaturation
  curves (C. Derst, Asparaginase from E. coli)

1. Non-constant fluorescence intensity as
observed parameter
32

• The upper and lower plateaus are not constants,
  but themself linear functions of c.

then expands to
33
DGs based on these values are very sensitive to
experimental errors!
DG (kJ/mol) m Literature 35.00.7 44.3
1.1 Calc 36.3 47.7
34
2. Remaining enzymatic activity dependent on
temperature instead of a denaturant
35
The basic form of the equation is the same,
because DG is linear in T, if DH and DS are
assumed constant within the observed temperature
range With no activity of the denatured state,
the familiar changes to
36
Temperature dependent measurements thus allow
determination of DG, DH and DS.
58.2C
58.4C
DG(25C)67.3 kJ/mol, DH672 kJ/mol
DG(25C)53.0 kJ/mol, DH809 kJ/mol
37
Averages and weighted averages Take a sample of
values vi 3.2, 3.5, 3.5, 4.0, 4.0, 4.0, 4.4 The
average v can be calculated for 7 values
(n7) or for 4 groups (n4) of values with
various occurrencies hi In a more general
case weights w(v) are used, that dont need to be
integer