Supporting Information for:
Combined Isothermal Titration and Differential Scanning Calorimetry Define
Three-State Thermodynamics of fALS-Associated Mutant Apo SOD1 Dimers
and an Increased Population of Folded Monomer
Helen R. Broom, 1 Kenrick A. Vassall, 1,2 Jessica A.O. Rumfeldt, 1 Colleen M. Doyle, 1 Ming Sze
Tong,1 Julia M. Bonner, 1,3 and Elizabeth M. Meiering 1*
1
Department of Chemistry, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
2
Present address: Department of Molecular and Cellular Biology, University of Guelph, Guelph,
Ontario, N1G 2W1, Canada
3
Present Address: Whitehead Institute for Biomedical Research, Cambridge, MA 02142, USA
Corresponding Author
*
Department of Chemistry, University of Waterloo, Waterloo, ON N2L 3G1, Canada. Tel.: 519-
888-4567, Ext. 32254; Fax: 519-746-0435; E-mail: [email protected]
1
Supplementary Methods
Models Used for Thermodynamic Analysis of Homodimeric Protein Folding. The simplest
model for the unfolding mechanism of a homodimeric protein is a reversible two-state transition
with concerted dissociation and unfolding of the native dimer (N 2) to unfolded monomers (U),
which can be expressed as:
𝐾(𝑇)
N2 ↔
2U
(S1)
[𝑁2 ] = 𝑃𝑑𝑖𝑚𝑒𝑟 (1 − 𝛼)
(S2)
[𝑈] = 2𝑃𝑑𝑖𝑚𝑒𝑟 (𝛼)
(S3)
where K(T) is the equilibrium constant for unfolding at any temperature T, Pdimer is the total
protein concentration in M dimer and α is the extent of the unfolding reaction. K(T) is defined as:
𝐾(𝑇) =
[𝑈]2
[𝑁2 ]
=
4𝑃 𝑑𝑖𝑚𝑒𝑟 𝛼 2
(S4)
(1−𝛼)
To determine the extent of the unfolding reaction at any temperature, eq S4 can be rearranged as:
𝛼=
−𝐾(𝑇)+√𝐾(𝑇)(𝐾(𝑇)+16𝑃𝑑𝑖𝑚𝑒𝑟 )
(S5)
8𝑃𝑑𝑖𝑚𝑒𝑟
𝑁
The heat capacities of the native ( 𝐶𝑝 2 ) and unfolded (𝐶𝑝𝑈 ) protein are usually taken to vary
linearly with temperature 1-4 (see Material and Methods):
𝑁
𝐶𝑝 2 = 𝐴 + 𝐵𝑡
(S6a)
𝐶𝑝𝑈 = 𝐸 + 𝐹𝑡
(S6b)
where A (E) and B (F) are the intercept and slope of the folded (unfolded) baseline and t is the
temperature in °C.
The change in heat capacity of unfolding (C p) can be determined at any temperature:
Cp(t) = (E – A) + (F – B)t
(S7)
2
The specific calorimetric enthalpy of the unfolding transition in cal (g protein)-1 as a function of
temperature can be written as:
𝑡
∆ℎ𝑐𝑎𝑙 (𝑡) = ∫𝑡
𝑟𝑒𝑓
∆𝐶𝑝 𝑑𝑡 = ∆ℎ𝑐𝑎𝑙 (𝑡𝑟𝑒𝑓 ) + (𝐸 − 𝐴)(𝑡 − 𝑡𝑟𝑒𝑓 ) +
1
2
2
(𝐹 − 𝐵)(𝑡 2 − 𝑡𝑟𝑒𝑓
)
(S8)
where tref is a reference temperature typically set at the temperature of half completion and
∆ℎ𝑐𝑎𝑙 (𝑡 𝑟𝑒𝑓 ) is the ∆ℎ𝑐𝑎𝑙 at tref. Note that when the pre and post transition baselines have the
same slope, the C p is constant with temperature and eq S8 simplifies to ∆ℎ𝑐𝑎𝑙 (𝑡) =
∆ℎ𝑐𝑎𝑙 (𝑡 𝑟𝑒𝑓 ) + (𝐸 − 𝐴)(𝑡 − 𝑡𝑟𝑒𝑓 ) which has been shown to be a reasonable approximation over
modest temperature intervals.1, 3, 5, 6
For fitting, hcal(t) is extrapolated to 0°C to give:
∆ℎ 0 = ∆ℎ𝑐𝑎𝑙 (𝑡𝑟𝑒𝑓 ) − (𝐸 − 𝐴)(𝑡𝑟𝑒𝑓 ) −
1
2
2
(𝐹 − 𝐵)(𝑡𝑟𝑒𝑓
)
(S9)
Now hcal can be calculated at any temperature t using:
∆ℎ𝑐𝑎𝑙 (𝑡) = ∆ℎ 0 + (𝐸 − 𝐴)𝑡 +
1
2
(𝐹 − 𝐵)𝑡 2
(S10)
The temperature-dependence of K is given by the van’t Hoff equation:
𝑑𝑙𝑛𝐾(𝑇)
𝑑𝑇
=
∆𝐻vH (𝑇)
where 𝛽 =
𝑅𝑇 2
=
∆𝐻vH (𝑇)
∆ℎcal (𝑇)
𝛽∆ℎ 𝑐𝑎𝑙 (𝑇)
(S11)
𝑅𝑇 2
and R is the gas constant, T is the temperature in units of Kelvin, and ΔH vH is
the van’t Hoff enthalpy for the change in enthalpy for unfolding. Note that ΔH vH has units of cal
(mol cooperative unit)-1 which, for this model, is cal (mol dimer)-1 and is distinct from the
calorimetrically determined change in enthalpy H cal =   hcal. ΔH vH reflects the steepness of
the transition and H cal is proportional to the area under the endothermic peak. Here, β is used as
a fitting parameter to allow these two terms to differ. In a strictly two-state transition the ratio of
3
ΔH vH to H cal is unity and β is equal to the molecular weight of the cooperative unit, in this case
the dimer. In non-2 state transitions, for example involving intermediate formation, the ratio < 1;
if samples are not normalized correctly for protein concentration the ratio can be higher or lower
than 1.
To obtain K as a function of temperature, eq S10 can be substituted into eq S11, integrated and
rearranged giving:
𝑇
∫𝑇
𝑅
𝛽
𝑟𝑒𝑓
𝑑 ln 𝐾(𝑇) = 𝑙𝑛
𝑙𝑛 (
𝐾(𝑇)
𝐾𝑟𝑒𝑓
𝐾
𝐾𝑟𝑒𝑓
1
1
𝑇
𝑇 𝑟𝑒𝑓
) = 𝐴𝐴 ( −
𝛽
=
𝑇
∫
𝑅 𝑇
∆ℎ𝑐𝑎𝑙 (𝑇)
𝑟𝑒𝑓
𝑇2
) + 𝐵𝐵𝑙𝑛 (
𝑇
𝑇 𝑟𝑒𝑓
𝑑𝑇
(S12)
) + 𝐶𝐶(𝑇 − 𝑇𝑟𝑒𝑓 )
(S13)
where:
1
(273.15)2 (𝐹 − 𝐵)
2
𝐵𝐵 ≡ (𝐸 − 𝐴) − (273.15)(𝐹 − 𝐵)
1
𝐶𝐶 ≡ (𝐹 − 𝐵)
2
𝐴𝐴 ≡ −∆ℎ 0 + 273.15(𝐸 − 𝐴) −
T = 273.15 + t
Solving for K gives,
1
1
𝑇
𝑇 𝑟𝑒𝑓
𝐾(𝑇) = 𝐾𝑟𝑒𝑓 × 𝑒𝑥𝑝 {[𝐴𝐴 ( −
) + 𝐵𝐵𝑙𝑛 (
𝑇
𝑇 𝑟𝑒𝑓
𝑅
) + 𝐶𝐶(𝑇 − 𝑇𝑟𝑒𝑓 )] ÷ }
𝛽
(S14)
The total measured heat capacity (C p,total) corresponds to a baseline heat capacity (C p,baseline) plus
the transition excess heat capacity resulting from the absorption of heat which drives the
unfolding reaction (C p,excess):
𝐶𝑝,𝑡𝑜𝑡𝑎𝑙 = 𝐶𝑝,𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 + 𝐶𝑝,𝑒𝑥𝑐𝑒𝑠𝑠
(S15)
C p,baseline is given by:
𝑁
𝐶𝑝,𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 = (1 − 𝛼(𝑡))𝐶𝑝 2 + 𝛼(𝑡)𝐶𝑝𝑈
(S16)
4
The C p,excess is given by:
𝜕𝛼
𝐶𝑝,𝑒𝑥𝑐𝑒𝑠𝑠 = ( ) ∆ℎ𝑐𝑎𝑙 (T)
(S17)
𝜕𝑇
The partial derivative
𝑑𝑙𝑛𝐾 (𝑇)
𝑑𝑇
=
∆𝐻vH (𝑇)
𝑅𝑇 2
=
𝜕𝛼
𝜕𝑇
can be solved analytically at any T (substituting K with eq S4):
𝛽∆ℎ𝑐𝑎𝑙 (𝑇)
𝑅𝑇 2
=
2 𝑑𝛼
𝛼 𝑑𝑇
+
1
𝑑𝛼
(S18)
1−𝛼 𝑑𝑇
which can be rewritten as:
𝑑𝛼
𝑑𝑇
=
𝛽∆ℎ𝑐𝑎𝑙 (𝑇) 𝛼(1−𝛼)
𝑅𝑇 2
(S19)
2−𝛼
Note that parameters such as ∆ℎ𝑐𝑎𝑙 are defined at a specific temperature regardless of the
temperature units so that ∆ℎ𝑐𝑎𝑙 (𝑇) is the same value as ∆ℎ𝑐𝑎𝑙 (𝑡). Combining S19 and S17, the
excess specific heat can be written as:
𝐶𝑝,𝑒𝑥𝑐𝑒𝑠𝑠 =
2
𝛽∆ℎ𝑐𝑎𝑙
(𝑡) 𝛼(1−𝛼)
𝑅𝑇 2
(S20)
2−𝛼
Dimer Three-State with Monomer Intermediate Unfolding Model. For homodimeric proteins,
more complex unfolding transitions may be observed. While many different unfolding
mechanisms are possible, thermal unfolding is often described using a three-state transition
model with a folded monomeric intermediate (M). This three-state transition model involves two
steps: (1) dimer dissociation, followed by (2) monomeric intermediate unfolding:
𝐾1 (𝑇)
𝑁2 ↔
𝐾2 (𝑇)
2𝑀 ↔
2𝑈
(S21)
[𝑁2 ] = 𝑃𝑑𝑖𝑚𝑒𝑟 (1 − 𝛼1 )
(S22)
[𝑀] = 2𝑃𝑑𝑖𝑚𝑒𝑟 𝛼1 (1 − 𝛼 2 )
(S23)
[𝑈] = 2𝑃𝑑𝑖𝑚𝑒𝑟 𝛼1 𝛼 2
(S24)
5
where K 1(T) and α1, and K 2(T) and α2 are the equilibrium constant and extent of the unfolding
reaction at any temperature for the first (N 2↔2M) and second (M↔U) unfolding transitions,
respectively.
𝐾1 (𝑇) =
𝐾2 (𝑇) =
[𝑀] 2
[𝑁2 ]
[𝑈] 2
[𝑀] 2
= 4𝑃𝑑𝑖𝑚𝑒𝑟
=
(S25a)
1−𝛼 1
𝛼2 2
(S25b)
(1−𝛼 2 )2
2
α1 =
1+ √1+
𝛼2 =
𝛼 1 2 (1−𝛼 2 )2
(S26a)
16𝑃𝑑𝑖𝑚𝑒𝑟
𝐾 1 (𝑇)(1+√𝐾 2 (𝑇))2
√ 𝐾2 (𝑇)
(S26b)
1+√ 𝐾2 (𝑇)
The specific heat capacity for M is assumed to be linear with temperature as for N 2 and U in eqs
S6a and S6b.
𝐶𝑝𝑀 = 𝐶 + 𝐷𝑡
(S27)
where C and D are the intercept and slope of the folded (unfolded) baseline.
The change in heat capacity of dimer dissociation (ΔC p,N2↔2M) and monomer unfolding
(ΔC p,M↔U) can be determined at any temperature:
ΔC p,N2↔2M (t) = (C – A) + (D – B)t
(S28a)
ΔC p,M↔U (t) = (E – C) + (F – D)t
(S28b)
Using the same procedure outlined in eqs S8-S14, the equations for K1 and K 2 as a function of
temperature are:
1
1
𝑇
𝑇 𝑟𝑒𝑓−1
1
1
𝑇
𝑇 𝑟𝑒𝑓 −2
𝐾1 (𝑇) = 𝐾𝑟𝑒𝑓−1 × 𝑒𝑥𝑝 {[𝐴𝐴1 ( −
𝐾2 (𝑇) = 𝐾𝑟𝑒𝑓−2 × 𝑒𝑥𝑝 {[𝐴𝐴2 ( −
) + 𝐵𝐵1𝑙𝑛 (
𝑇
𝑇 𝑟𝑒𝑓−1
) + 𝐵𝐵2𝑙𝑛 (
where:
6
𝑇
𝑇 𝑟𝑒𝑓−2
𝑅
) + 𝐶𝐶1(𝑇 − 𝑇𝑟𝑒𝑓−1 )] ÷ } (S29a)
𝛽
𝑅
) + 𝐶𝐶2(𝑇 − 𝑇𝑟𝑒𝑓−2 )] ÷ } (S29b)
𝛽
1
(273.15)2 (𝐷 − 𝐵)
2
𝐵𝐵1 ≡ (𝐶 − 𝐴) − (273.15)(𝐷 − 𝐵)
1
𝐶𝐶1 ≡ (𝐷 − 𝐵)
2
𝐴𝐴1 ≡ −∆ℎ10 + 273.15(𝐶 − 𝐴) −
1
(273.15)2 (𝐹 − 𝐷)
2
𝐵𝐵2 ≡ (𝐸 − 𝐶) − (273.15)(𝐹 − 𝐷)
1
𝐶𝐶2 ≡ (𝐹 − 𝐷)
2
𝐴𝐴2 ≡ −∆ℎ20 + 273.15(𝐸 − 𝐶) −
and Kref-1 and K ref-2 are the equilibrium constants at the reference temperatures for dimer
dissociation and monomer unfolding, respectively (which in the present study we take to be the
experimental temperature for measurement of K ref-1 i.e. 37 C, and the temperature of the
midpoint for monomer unfolding where K ref-2 =1, respectively, see below and Table S1).
Using eqs S18, S25a and S25b:
𝑑𝛼1
𝑑𝑇
𝑑𝛼2
𝑑𝑇
=(
=
𝛽1 ∆ℎ𝑐𝑎𝑙1 (𝑇)
𝑅𝑇 2
𝛽2 ∆ℎ𝑐𝑎𝑙2 (𝑇)
2𝑅𝑇 2
+
𝛼 2 𝛽2 ∆ℎ 𝑐𝑎𝑙2 (𝑇)
𝑅𝑇 2
)
𝛼 1 (1−𝛼 1 )
(S30a)
2−𝛼1
× 𝛼 2 (1 − 𝛼 2 )
(S30b)
For simplicity the subscripts 1 and 2 were used for the parameters  and hcal as well as , to
refer to dimer dissociation and monomer unfolding, respectively, so that ∆ℎ𝑐𝑎𝑙1 
∆ℎ𝑐𝑎𝑙𝑁2 ↔2𝑀 and ∆ℎ𝑐𝑎𝑙2  ∆ℎ𝑐𝑎𝑙𝑀↔𝑈 . Also:
𝐶𝑝,𝑒𝑥𝑐𝑒𝑠𝑠 =
𝑑𝛼 1
𝑑𝑇
∆ℎ𝑐𝑎𝑙1 (𝑡) + (
𝑑𝛼 1
𝑑𝑇
𝛼2 +
𝑑𝛼 2
𝑑𝑇
𝛼1 ) ∆ℎ𝑐𝑎𝑙2 (𝑡)
𝑁
𝐶𝑝,𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 = 𝑓𝑁2 𝐶𝑝 2 + 𝑓𝑀 𝐶𝑝𝑀 + 𝑓𝑈 𝐶𝑝𝑈
(S31)
(S32)
where 𝑓𝑁2 , 𝑓𝑀 and 𝑓𝑈 are the fractions of native dimer, monomer intermediate and unfolded
monomer, respectively, and can be calculated using:
7
𝑓𝑁2 =(1−𝛼1 )
(S33a)
𝑓𝑀=𝛼1 (1−𝛼2 )
(S33b)
𝑓𝑈=𝛼1 𝛼2
(S33c)
where
𝑓𝑁2 + 𝑓𝑀 + 𝑓𝑈 = 1
(S33d)
Methods for Simplifying the Dimer Three-State with Monomer Intermediate Unfolding Model.
Due to the additional parameters in the three-state model compared to the two-state model,
fitting individual thermograms to eq 3 resulted in high uncertainties in the fitted values.
Accordingly, multiple datasets were fit globally (Matlab R2013b, The MathWorks Inc.) using
shared parameters. The slopes of the monomer intermediate and unfolded monomer baselines
were set equal to that of the native baseline (i.e., B=D=F), making the common assumption that
ΔCp of unfolding is temperature independent (Figure S3),1,
3, 5
which has been shown to be
reasonable over limited temperature ranges as used here. 7 The intercepts of the intermediate (C)
and unfolded (E) baselines were defined relative to the intercept of the native baseline using
temperature-independent values for the change in heat capacity upon dimer dissociation to
monomer intermediate (ΔC p,N2↔2M) and the change in heat capacity upon monomer intermediate
unfolding (ΔCp,M↔U):
C= A + ΔC p,N2↔2M
(S34a)
E= A + ΔCp,N2↔2M + ΔC p,M↔U
(S34b)
ΔCp,N2↔2M was set to 1.7 kcal (mol dimer)-1 °C -1 (and the corresponding value in units of kcal g-1
°C -1 obtained by dividing by the molecular weight of the dimer), the average value measured
8
using Kirchoff analysis of ITC data for SOD1 variants where the enthalpy of dimer dissociation
was measured as a function of temperature. 4, 8, 9 For the three-state model, ΔC p,N2↔2M + ΔCp,M↔U
= ΔC p.N2↔2U (total ΔCp of apo SOD1 unfolding from folded dimer to unfolded monomers); the
value of ΔC p,M↔U was obtained by subtracting ΔC p,N2↔2M from the experimentally determined
value for ΔC p,N2↔2U of 3.3 kcal (mol dimer)-1 °C -1,1 which gives a value of 1.6 kcal (mol dimer) -1
°C -1 or 0.8 kcal (mol monomer)-1 °C-1. This approach is consistent with the observations that
mutations typically cause little change in ΔC p 4, 10 and that the average directly fitted values of
ΔCp,N2↔2U for apo SOD1 mutants (Table 1) are close to the value of 3.3 kcal (mol dimer) -1 °C -1
determined for pWT and G93 mutants.11,
12
Of note, lower values of ΔC p,N2↔2U for A4V and
V148G (Table 1) are likely related to increased monomer formation, which is most pronounced
for these dimer interface mutants (Figure 1).
To further simplify the fitting, the parameters of the first transition (dimer dissociation) were
fixed to values determined by ITC (Figure S1).10 Specifically, the Kref-1 was set to the value
measured by ITC, K d,N2↔2M, and the associated tref-1 (Tref-1) was fixed to 37 °C (310.15 °K), the
temperature where ITC was performed. The ∆ℎ𝑐𝑎𝑙1 (𝑡𝑟𝑒𝑓−1 ) was fixed to the value determined
by ITC at 37°C, ∆ℎ𝑐𝑎𝑙𝑁2 ↔2𝑀 . Thus, in fitting data to eqs S31 and S32, the globally shared fitted
parameters were: 𝑡𝑟𝑒𝑓−2 , ∆ℎ𝑐𝑎𝑙2 (𝑡𝑟𝑒𝑓−2 ) (same as ∆ℎ𝑐𝑎𝑙𝑀 ↔𝑈 (𝑡𝑟𝑒𝑓−2 )), β1 = β2, and parameters
defining the slope and intercept of the native baselines.
Two-State Monomer Unfolding Model. DSC data for apo mutants showing evidence for
significant monomer formation (A4V, H46R, and V148G) were also analyzed using a monomer
two-state unfolding model describing a reversible transition from folded monomer (M) to
9
unfolded monomers (U), M↔U.4 Individual thermograms were fit (using Origin 5.0, Microcal
Inc) to eq S35:
𝐶𝑝 = (𝐶 + 𝐷𝑡)(1 − 𝛼) + (𝐸 + 𝐹𝑡)𝛼 +
2
𝛽∆ℎ 𝑐𝑎𝑙
(𝑡 0.5 )𝛼(1−𝛼)
(S35)
𝑅𝑇 2
where C p is the total specific heat absorption at temperature t (in °C); C and E are the intercepts
of the folded and unfolded baselines, respectively; D and F are the slopes of the folded and
unfolded baselines, respectively; R is the universal gas constant; β is the ratio of van’t Hoff to
calorimetric enthalpy multiplied by the molecular weight of the SOD dimer; Δhcal is the specific
calorimetric enthalpy of unfolding at t; α is the extent of the unfolding reaction; and t0.5 is the
temperature at which unfolding is half complete (i.e α =0.5).
Predicting ΔC p,N2↔2M Based on Changes in Solvent Accessible Surface Area (ΔASA).
The
polar and non-polar contributions to ΔASA (ΔASAp andΔASAnp, respectively) between dimer and
dissociated monomers were determined using the crystallographic structures for apo SOD1 wildtype (1HL4) using:
ΔASAp = ASAmonA-p + ASA monB-p – ASAdimer-p
(S36a)
ΔASAnp = ASAmonA-np + ASAmonB-np – ASAdimer-np
(S36b)
where ASA monA-p and ASA monB-p are the polar, ASAmonA-np and ASAmonB-np are the non-polar solvent
accessible surface areas of the folded monomers A and B, respectively, which together make up
the dimer in the crystal structure, and ASA dimer-p and ASA dimer-np are the polar and non-polar
solvent accessible surface areas, respectively, of the folded dimer. These values were calculated
using InterProSurf.1
10
The ΔC p,N2↔2M can be predicted using ΔASAp and ΔASAnp and the empirically derived
equations:
ΔCp,N2↔2M = -0.32 x ΔASAnp + 0.14 x ΔASA p 13
(S37a)
ΔCp,N2↔2M = -0.45 x ΔASAnp + 0.26 x ΔASA p 14
(S37b)
ΔCp,N2↔2M = -0.28 x ΔASAnp + 0.09 x ΔASA p 15
(S37c)
ΔCp,N2↔2M = -0.51 x ΔASAnp + 0.21 x ΔASA p 5
(S37d)
An average ΔC p,N2↔2M value of 0.45 ± 0.12 kcal (mol dimer) -1 °C -1 was determined based on eqs
S37a-d and using predicted ΔASA np and ΔASAp of 1262 Å 2 and 258 Å 2, respectively. 16
Calculation of Thermodynamic Parameters. Assuming a temperature-independent ΔC p, which
has been shown to be a reasonable approximation over modest temperature intervals 17 the ΔH as
a function of temperature is:
∆𝐻(𝑇) = ∆𝐻(𝑇𝑟𝑒𝑓 ) + ∆𝐶𝑝 (𝑇 − 𝑇𝑟𝑒𝑓 )
(SA1)
where Tref is a reference temperature in degrees Kelvin, and ΔH(Tref) and ΔH(T) are the change
in enthalpy of unfolding at Tref and T, respectively, noting again that T  t + 273.15 and ΔH(Tref)
is the same value as ΔH(tref).
The temperature-dependence for the change in entropy for
unfolding, ∆S, is given by:
∆𝑆(𝑇) = ∆𝑆𝑟𝑒𝑓 + ∆𝐶𝑝 ln (
𝑇
𝑇 𝑟𝑒𝑓
)
(SA2)
The above equations can be combined to give the Gibbs-Helmholtz equation:
∆𝐺(𝑇) = −𝑅𝑇 ln 𝐾(𝑇) = ∆𝐻(𝑇𝑟𝑒𝑓 ) (1 −
𝑇
𝑇 𝑟𝑒𝑓
) + ∆𝐶𝑝 [𝑇 − (𝑇𝑟𝑒𝑓 ) − 𝑇 ln (
11
𝑇
𝑇 𝑟𝑒𝑓
)]
(SA5)
The calculations for figures and tables were performed as follows using information in Table S1.
1. H cal at tref in cal (mol dimer)-1 was calculated by multiplying hcal(tref) by the corresponding
.
2. G as a function of temperature was calculated using eq SA5 and the associated H cal and
Cp.(refer to Table S1).
3. Fractions (f) were calculated by solving the quadratic equations using equilibrium constants
for the associated transitions (K 1, K 2) calculated as a function of temperature using the
corresponding G values. For each temperature, fU (two-state) or fM (three-state) were determined
by solving the quadratic equation using the equilibrium constants K (two -state) or K 1 and K 2
(three-state) which were calculated from G at each temperature using equation SA5 and a given
protein concentration. For the three-state model, fU was then calculated knowing fU = fMK2. The
fraction of the final species fU (two -state) and fN2 (three-state) were determined knowing they
add to 1.
4. As a check, fractions were also calculated for the dimer three-state model using eqs S33a-c,
S26a,b and S29a,b using the appropriate fitted or fixed parameters given in Table S1. For the
dimer two-state model, fractions can also be calculated by using the  values and eqs S5 and S14
where 𝑓𝑁2 = (1 − 𝛼) and 𝑓𝑈 = 𝛼.
12
Supplementary Results
We used several approaches to assess the uncertainties in monomer stability as well as total
protein stability for the three-state fits. Because the ΔC p,N2↔2M could not be measured for all
SOD1 variants due to low heats of dissociation at low temperature, the data were also fit with the
maximum ΔC p,N2↔2M determined experimentally (2.2 kcal (mol dimer)-1 °C-1)1, 3, 5 corresponding
to an estimated upper limit of mutational effects, to evaluate how changes in ΔC p may impact
monomer stability. In general, mutations have been found to have little effect on ΔC p for global
protein unfolding (ΔC p,N2↔2U),10 and ITC experiments show that ΔCp,N2↔2M also varies little upon
mutation of SOD1. 4,
7, 11, 12
Highly non-conservative substitutions at buried positions of
hydrophobic residues by hydrophilic residues or vice versa have, however, been reported to
change ΔC p by up to ~40%.10 We found that comparable increase in ΔC p,N2↔2M (by ~0.6 kcal
(mol dimer)-1 °C -1 with simultaneous decrease of ΔC p,M↔U by 0.3 kcal (mol monomer) -1 °C -1 to
keep ΔC p,N2↔2U constant as 3.3 kcal (mol dimer)-1 °C -1) has relatively small effects on ΔG M↔U
calculated at the tavg of 51.2 °C (on average ±0.1 kcal (mol monomer)-1) and at 37 °C (on average
±0.2 kcal (mol monomer)-1). Because dimer dissociation was measured at 37 °C, changes in
ΔCp,N2↔2M have no effect on ΔG N2↔2M(37 °C), whereas ΔG N2↔2M(tavg) is decreased by ~0.2 kcal
(mol dimer)-1. Thus, for three-state fitting of DSC data, treating ΔC p as a constant is further
substantiated as reasonable, and changes in ΔC p have little impact on monomer stability.
We also confirmed that potential aggregation at high temperature, which we also
examined previously, 18 has little effect on fitted values, by varying the amounts of fitted data
beyond the peak of the unfolding endotherm from a maximum of the apparent end of the
endotherm peak to a minimum of ~25% of the high temperature side of the endotherm. Fitting
13
various amounts of the endotherm to the three-state model has little impact on total stability:
±0.2-0.4 kcal (mol dimer)
-1
at tavg, and ±0.5-1.0 kcal (mol dimer)-1 at 37 °C. Also, similar
stability values were obtained when ΔH vH and ΔH cal were set to equal to each other (Table S1).
Based on these analyses, effects of aggregation can be effectively minimized by excluding high
temperature data from the fit, with little effect on the measured stability.
14
Table S1. Treatment of parameters for DSC data fitting to dimer unfolding
modelsa
parameters
two-state
N 2↔2U
tref
hcal(tref)
°C
cal g-1

g mol-1
A
B
C
D
E
F
cal g-1 °C-1
cal g-1 °C-1
cal g-1 °C-1
cal g-1 °C-1
cal g-1 °C-1
cal g-1 °C-1
M dimer
Pdimerc
Kref d
Cp
kcal (mol
dimer)-1 °C-1
three-state
N 2↔2M (1)
M↔U (2)
t0.5, fita
fit
37°C
fit
MWdimer
fit
or fit with 1 =2
fit
fit
fit
fit
A + ΔCp,N2 ↔2M
fit
B
B
nab
na
na
na
fixed
fixed
For calculations:
2Pdimer
KITC
3.3
1.7
2
t0.5, fit
fit
MWdimer
or fit with 1 =2
na
na
A + ΔCp,N2 ↔2M
B
C + ΔCp,M↔U
B
fixed
1
1.6
2
4Pdimer(fM ) + K1 (1+K2)f M – K1
fU = f M K2
1=
fN2 + fU
fN2 + fM + fU
a
The parameters for global fits using the dimer two-state or the dimer three-state with
monomeric intermediate models were set to defined values or allowed to float and so fit as
specified above. bna indicates not applicable. cProtein concentration fixed to values determined
by UV absorbance. Although endotherms were normalized by g protein, the fitting equation
uses units of M dimer. The molecular weight of SOD1 used for pWT and mutants (MW dimer)
was 31500 g/mol. d The Kref is not a fit parameter but is defined for each model.4,6
0=
4Pdimer(fU ) + K(fU ) - K
15
Table S2. Thermodynamic parameters for apo SOD1 determined from global three-state fits using different shared parameters.
∆HN
SOD1
varianta
2
↔2M
∆GN
↔2M
2
t0.5, M↔U
(°C)c
∆HM↔U
(kcal (mol
monomer)-1)
tavgc,d
∆GM↔U
(kcal (mol
monomer)-1)
37 °Ce,f
∆GM↔U
(kcal (mol
monomer)-1)
tavgd, f
∆∆GM↔U
(kcal (mol
monomer)-1)
tavgd,g
na
na
3.4 ± 0.5
na
na
pWTc,h
(kcal (mol
dimer)-1)
37 °Cb
na
(kcal (mol
dimer)-1)
37 °Cb
10.2 ± 0.7
pWT
(30.8 ± 8.8)
(10.3 ± 0.5)
59.5 ± 0.9
44.0 ± 2.0
2.8 (3.0, 1.9)
1.2 (1.3, 0.7)
na
pWTi
8.8 ± 13.5
9.0 ± 11.8
58.4 ± 0.9
49.1 ± 6.7
3.0
1.10
na
V148I
(11.4 ± 2.2)
(8.9 ± 0.2)
60.1 ± 0.2
84.0 ± 1.2
5.7 (5.7, 4.2)
2.3 (2.4, 1.6)
-1.2
V148Ii
7.5 ± 3.8
7.7 ± 3.2
60.0 ± 0.1
79.9 ± 3.2
5.4
2.18
nd
G93S
(17.6 ± 4.6)
(8.4 ± 0.3)
49.2 ± 1.1
58.3 ± 3.7
2.0 (2.0, 1.5)
-0.4 (-0.3, -0.6)
1.5
H46R
(16.2 ± 4.4)
(8.4 ± 0.4)
62.5 ± 0.1
71.2 ± 1.1
5.3 (5.4, 4.7)
2.6 (2.6, 2.3)
-1.4
H46R
25.0 ± 3.0
8.7 ± 3.1
62.8 ± 0.1
70.0 ± 1.9
5.3
2.5
nd
E100G
(16.0 ± 4.8)
(8.0 ± 0.4)
48.0 ± 0.7
53.3 ± 8.4
1.6 (1.6, 2.1)
-0.5 (-0.4, -0.3)
1.7
G37R
(7.8 ± 1.8)
(7.6 ± 0.2)
50.3 ± 0.1
84.1 ± 2.8
3.2 (1.8, 3.0)
-0.2 (-0.3, -0.3)
1.4
G37Ri
42.7 ± 26.5
10.3 ± 15.6
46.7 ± 0.8
55.4 ± 21.6
1.5
-0.8
nd
H43R
(23.0 ± 1.4)
(7.5 ± 0.0)
47.6 ± 0.4
59.5 ± 5.2
1.7 (1.7, 1.9)
-0.6 (-0.6, -0.6)
1.8
G93A
(14.0 ± 2.0)
(7.2 ± 0.3)
47.4 ± 0.3
58.9 ± 4.7
1.7 (1.7, 1.7)
-0.7 (-0.6, -0.7)
1.9
G93Ai
22.0 ± 10.6
8.1 ± 3.8
46.1 ± 0.7
50.8 ± 5.4
1.3
-0.8
nd
I113T
(30.2 ± 2.5)
(7.1 ± 0.2)
46.7 ± 0.2
53.2 ± 3.7
1.4 (1.5, 1.7)
-0.7 (-0.6, -0.7)
1.9
I113Ti
27.2 ± 4.3
7.8 ± 1.3
45.7 ± 0.4
50.7 ± 1.7
1.2
-0.9
1.9
A4T
(39.2 ± 3.8)
(7.1 ± 0.2)
43.6 ± 0.4
48.9 ± 9.6
0.8 (0.9, 1.3)
-1.1 (-1.0, -1.1)
2.3
i
A4T
13.7 ± 46.3
10.4 ± 17.4
30.0 ± 6.4
42.9 ± 50.2
-0.8
-2.6
nd
A4S
(9.0 ± 2.6)
(7.0 ± 0.0)
46.3 ± 0.4
61.1 ± 10.0
1.5 (1.1, 1.0)
-0.9 (-1.2, -1.3)
2.1
A4Si
46.5 ± 14.0
9.0 ± 4.1
45.5 ± 1.7
45.0 ± 6.6
1.1
-0.8
nd
i
16
G93R
(45.6 ± 1.8)
(6.7 ± 0.1)
49.1 ± 0.2
87.8 ± 7.7
3.1 (3.1, 2.9)
-0.6 (-0.5, -0.5)
1.7
A4V
(37.2 ± 3.8)
(6.4 ± 0.3)
50.9 ± 0.2
59.2 ± 3.4
2.3 (2.2, 2.4)
-0.1 (-0.1, -0.1)
1.2
A4V
35.9 ± 5.4
6.8 ± 2.2
51.0 ± 0.4
55.9 ± 3.6
2.3
0.0
nd
V148G
(50.6 ± 1.4)
(5.9 ± 0.3)
48.6 ± 0.0
67.8 ± 0.5
2.2 (2.3, 2.1)
-0.5 (-0.5, -0.5)
1.7
i
V148Gi
54.8 ± 0.4
5.7 ± 0.2
48.6 ± 0.0
65.7 ± 0.3
2.2
-0.5
nd
a
na, not applicable; nd, not determined. For each mutant, the scans at different protein concentrations used in the global fitting are those listed in Table 1, with the
exception of pWT, where concentrations 0.20, 0.21, 0.40, 0.44, 0.85, 1.50, and 3.0 were fit. bNumbers in the brackets were determined by ITC and fixed in the DSC
three-state fits. cErrors are the uncertainty in fitted values. dtavg is 51.2 °C, the average of all t0.5 values obtained from the two-state fits (Table 1). eΔGM↔U values
calculated at physiological temperature. fValues are determined from fits allowing ΔHvH/ΔHcal to vary. Monomer stability was also determined using a higher ΔCp,N2↔2M
(2.2 kcal (mol dimer)-1 °C-1), and these values are the first values shown in brackets. Data were also fit with ΔHvH and ΔHcal set equal, and these are the second values
shown in brackets. Uncertainties in monomer stability were approximated from the range of values obtained from these 3 different fitting procedures (Table 2). gΔΔG =
ΔGpWT - ΔGmutant, a positive value indicates lower stability of the mutant relative to pWT; values are calculated at tavg, where monomer stability is best defined. hΔGN ↔2M
2
and ΔGM↔U were also determined by globally fitting urea denaturation curves at 37 °C to a three-state model with monomer intermediate. iΔGM↔U values obtained by
fitting additional parameters ΔHN2↔2M and ΔGN2↔2M (ie. not fixing these parameters to the values obtained by ITC) and setting ΔHvH and ΔHcal equal, for mutants with
more than 3 datasets. This fitting method returns values with high uncertainty; therefore, the values from the fixed fits give more reliable comparison of relative
stabilities.
17
Table S3. Thermodynamic parameters for monomer two-state unfolding of apo SOD1.
∆Cp,M↔U
∆HvH (t0.5)
SOD1
[SOD1]
t0.5
(kcal (mol
(kcal (mol
-1
a
variant
(mg mL )
(°C)
monomer)-1 )
monomer)-1 ) a
A4V
0.20
51.5 ± 1.4
-1.15
45.5 ± 10.6
a
A4V
0.30
50.3 ± 0.6
0.02
56.6 ± 7.9
A4V
0.40
50.6 ± 0.3
-0.47
56.9 ± 5.1
A4V
0.50
50.8 ± 0.2
0.29
54.7 ± 2.5
A4V
1.00
50.3 ± 0.4
0.26
65.9 ± 4.4
A4V
1.95
51.5 ± 0.1
-0.18
79.3 ± 2.6
H46R
0.08
61.6 ± 1.3
1.55
73.0 ± 18.8
H46R
0.17
61.9 ± 0.3
0.71
74.6 ± 6.6
H46R
0.32
62.2 ± 0.1
1.01
84.6 ± 2.2
H46R
0.39
62.2 ± 0.2
0.27
86.6 ± 4.7
H46R
0.76
62.2 ± 0.1
1.07
94.9 ± 2.5
V148G
0.12
47.1 ± 0.5
5.19
44.7 ± 4.3
V148G
0.23
51.1 ± 0.1
-1.68
62.3 ± 0.6
V148G
0.29
52.3 ± 0.0
-3.07
52.4 ± 0.3
V148G
0.53
49.8 ± 0.0
-0.76
61.0 ± 0.2
V148G
0.92
49.2 ± 0.0
-0.71
59.2 ± 0.1
V148G
1.56
48.4 ± 0.0
-0.51
55.6 ± 0.8
Uncertainty estimates in fitted parameters are from the fitting program.
18
Figure S1. Representative raw ITC data obtained at 37 °C for SOD1 mutants. (A) G93R, (B)
H43R and (C) I113T. Each peak represents the measured heat for a small volume injection of
protein solution into the ITC sample cell. The heat associated with each injection (qi) was
determined by integrating the power versus time trace. Data were fit to a dimer dissociation
𝑣
𝑣
𝑉
𝑉
model10, 19, 20 according to 𝑞𝑖 = 𝑉∆𝐻𝑑 ([𝑀𝑖 ] − [𝑀𝑖−1 ] (1 − ) − 𝑓𝑚 [𝑀𝑜 ] ) + 𝑞𝑑𝑖𝑙 , where ΔH d
is the enthalpy change of dissociation from native dimer to two monomers, calculated per mol
monomer. [M]o is the total concentration of apo SOD1 (monomer units) in the syringe, [M i] and
[M i-1] are the concentrations of apo SOD1 monomer in the ITC cell after injection i and i-1,
respectively, v is the volume of each injection, V is the ITC reaction cell volume, qdil is a
correction factor for the heat associated with sample dilution unrelated to dissociation, and fm is
the fraction of protein in the syringe that exists as free monomer, which can be expressed as
19
𝑓𝑚 =
1
4[𝑀0 ]
2
(−𝐾𝑑 + √ 𝐾𝑑 + 8𝐾𝑑 [𝑀𝑜 ]). The data were fit using Microcal Origin 7.0 (Microcal
Inc) with ΔH d, K d and qdil as floating parameters.
20
Figure S2. Plots of lnPdimer versus 1/T0.5 used to determine molecularity, n, for apo SOD1
variants. The lnPdimer values are plotted versus 1/T0.5 values from the dimer two-state fits for a
representative set of apo variants (Table 1), and fit to a straight line using linear regression. Note
that the midpoint of the thermal unfolding transition is a relatively well defined experimental
value that is affected little by fitting to different unfolding models. The values of slope from
these linear fits were used to determine n (summarized in Table 1) using eq 2, as described in the
Material and Methods. Values of n are related to the inverse of the slope values. In this plot, the
data for H46R and A4V have the steepest slopes, and hence the lowest average n values of ~1.3
and ~1.6, respectively, consistent with these mutants having higher populations of monomer
(Figure 7). The lower slopes for the other SOD1 variants correspond to higher n values
approaching ~2, consistent with predominantly dimer unfolding. When molecularities were
calculated using ∆H cal similar trends were observed but there was more scatter in the data, likely
relating to the typically higher experimental error in ∆H cal.21 Taken together, the molecularity
analyses are consistent with dimer unfolding with varying levels of monomer, in agreement with
trends in t0.5 values with protein concentration (Figure 3, Table 1).
21
Figure S3. Three-state thermal denaturation of apo SOD1. The parameters for each transition in
the total heat of unfolding (black curve) can be used to simulate endotherms for two separate
protein transitions, dimer dissociation (red curve) and monomer unfolding (blue curve). In the
three-state global fitting approach used here, K 1 (same as K d,N2↔2M) and ∆ℎ𝑐𝑎𝑙1 (same as
∆ℎ𝑐𝑎𝑙𝑁2 ↔2𝑀 ) which characterize dimer dissociation, were set to the values determined by ITC at
37 °C. The slopes of the monomer intermediate and unfolded monomer baselines were set equal
to that of the native baseline, making the common assumption that ΔC p of unfolding is
temperature independent.4, 22 The intercepts of the intermediate and unfolded baselines were
defined relative to the intercept of the native baseline (solid grey line) according to temperature independent values for ΔC p,N2↔2M and ΔC p,M↔U (see Materials and Methods). Thus, the unfolded
monomer and dimer baselines, grey dashed and dotted lines respectively, were defined based on
∆Cp,N2↔2M 1.7 kcal (mol dimer) -1 °C-1 and ∆C p,M↔U 1.6 kcal (mol dimer) -1 °C-1; The only floating
parameters were tref-2 and ∆ℎ𝑐𝑎𝑙2 (𝑡𝑟𝑒𝑓−2 ) (same as ∆ℎ𝑐𝑎𝑙𝑀↔𝑈 (𝑡𝑟𝑒𝑓−2 )), β1 = β2, and parameters
defining the intercept (A) and slope (B) of the native baselines (solid grey line). Note, because of
the way the baselines are defined, the blue and red traces do not add to make black as they do in
Figure 7 with baselines subtracted.
22
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