Transcript Differential Scanning Calorimetry (DSC) intro

DSC: Data Analysis
Michael Blaber
Professor of Biomedical Sciences
College of Medicine
Florida State University
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Outline
• Thermodynamic parameters
• Model properties and assumptions
• Error
• Some examples
• Consider protein as the biomolecule of interest
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Thermodynamic parameters
A simple DSC “endotherm”:
• Buffer/buffer run subtracted
• Normalized for concentration
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• Native state is a “solid-like” phase under “low” temperature
conditions
• CpN(T) is the native state heat capacity function
CpN(T)
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• Denatured state is a “liquid-like” phase under “high” temperature
conditions
• CpD(T) is the denatured state heat capacity function
CpD(T)
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• The system transitions from the CpN(T) to the CpD(T) heat
capacity function as the protein undergoes a temperaturedependent “phase” transition (from “solid-like” to “liquid-like”)
CpN(T) to CpD(T) Function Transition
“DSC Baseline”
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• The “excess enthalpy” represents the heat energy associated
with the “phase” transition (heat of “fusion”)
• DHcal is also known as the “calorimetric enthalpy” of unfolding
The integrated area represents DHcal
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• The midpoint of the transition from the N to D state is the
“melting temperature” or Tm
(the Tm is not necessarily the
apparent maximum of the
excess enthalpy)
Tm
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• CpD(T)-CpN(T) = DCp(T) (“delta” values always state2-state1)
• DCp(T) is a characteristically positive value for protein
denaturation (i.e. CpD(T) > CpN(T) @ Tm)
DCp(T) @ Tm
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DCp(Tm) is a characteristically positive value for protein denaturation
• Protein denaturation exposes formerly buried hydrophobic
groups to solvent
• Solvent forms an organized clathrate structure around these
hydrophobic groups
• This organized solvent is a low entropy situation, with the
ability to substantially increase in disorder, resulting in a high
heat capacity
Some proteins can unfold to an intermediate that lacks substantial
secondary structure (i.e. secondary structure has been “melted”) but
retains a conformation that shields many hydrophobic groups from
solvent.
• The apparent DCp(Tm) in this case will have a very low value
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Summary of basic thermodynamic parameters
• CpN(T) Native state heat capacity function
• CpD(T) Denatured state heat capacity function
• DCp(T) = CpD(T)-CpN(T)
• DCp(@Tm) “Delta Cp”
• Tm “Melting temperature”
• The temperature at which protein is 50% folded
• Keq = 1.0, and thus DG(Tm)=0
• DHcal “Calorimetric enthalpy”, “enthalpy of unfolding”, DH(@Tm)
• DH(T) can be derived
• DS(@Tm) = DHcal/Tm “entropy of unfolding”
• DS(T) can be derived
• DG(T) can be derived
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Model properties and assumptions
Typically, the common models used to fit DSC data have the following
three important assumptions:
• The system is reversible
• The system is in equilibrium
• The system is two-state (N and D states)
If the assumptions of the model are not met (i.e. verified) then the
derived parameters are potentially in error
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Assumption 1: The system is reversible
• Aggregation is an irreversible pathway from the denatured (or
partially denatured) state
N  D  Aggregation
• Lack of visible aggregation does not mean system is reversible
• Reversibility is confirmed by recovery of the enthalpy of unfolding
upon cooling and subsequent reheating
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Initial Scan
Subsequent scan
Pronounced (asymmetric)
exotherm following initial
endotherm
CpD < CpN (i.e. negative DCp)
“Dead” second scan
Post-transition noise
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Initial Scan
Subsequent scan
No sharp exotherm
Recovery of
substanital enthalpy
on second scan
CpD > CpN (i.e. positive DCp)
No post-transition
noise
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Assumption 2: The system is in equilibrium
• The scan rate must not be faster than the kinetics of the phase
transition (folding/unfolding rates)
• Most DSC instruments have a default scanrate of 60°/hr, this may be
too fast for some proteins (b-sheet) and scan rates of <15°/hr may be
necessary in such cases.
• Equilibrium is confirmed by an absence of hysteresis when
comparing up-scans and down-scans
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Hysteresis with up/downscans at 60°/hr
(traces inverted for
ease of identification)
No hysteresis with up/
downscans at 15°/hr
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Assumption 3: The system is two-state (N and D states)
• Common models to analyze DSC data assume monomeric two-state
denaturation.
• The following situations will violate the assumptions of the model
and result in erroneous analyses:
NID
N2  2D
• Two-state unfolding is confirmed by
• The absence of systematic residual error to a two-state fit
• A characteristic positive value for DCp
• Agreement between DHcal with DH determined from a two-state
model (i.e. DHvH – “the van’t Hoff enthalpy”)
NID
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• System denaturation is too broad for a two state model
Fit overshoots at maximum
Fit undershoots at shoulders
DCp(Tm)
abnormally low
Residual endothermic signal
NID
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Plot of residual error to a 2-state fit (i.e. fit – raw data):
Tm
• Obvious systematic
error centrosymmetric
at the Tm
• with NEG peak @ Tm
NID
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van’t Hoff enthalpy (DHvH):
• Calculation of DH (and DS) based upon Keq assuming two-state
system:
DH – TDS = -RTlnKeq
• DHvH < DHcal for non-2-state systems with a folding intermediate
• DHvH/DHcal < 1.0 for non-2-state systems with a folding
intermediate
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Oligomers:
N2  2D
• Similar situation (i.e. systematic error in the residual, centrosymmetric at
the Tm), but the model fit would undershoot at the Tm and overshoot on the
shoulders (i.e. characteristic POS peak for the residual at the Tm)
• DHvH > DHcal
• DHvH/DHcal > 1.0
The basic take-home message:
If the systematic error (i.e. the residual plot) is significantly greater
than the expected instrument error (i.e. point to point error) then the
2-state assumption is not supported
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Error
Baselines… (CpN(T) and CpD(T) functions)
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Low temperature regime is
experimentally accessible
Extrapolated
Error in CpN(T)
CpN(T)
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Extrapolated
Error in CpD(T)
CpD(T)
High temperature regime is
experimentally accessible
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Additional concerns regarding CpN(T) and CpD(T) baselines:
DG = DH – TDS = -RTlnKeq
• The equilibrium describes a continuum of N and D partitioning with Temp
• There may be a temperature regime where the N state is
substantially populated, but there is no temperature where the N
state is 100% populated (similarly, with D state).
• You can assign a temperature of maximum DG but you cannot
define the temperature where the protein “begins to unfold”
• How to assign CpN(T) and CpD(T) with confidence?
Some fitting routines require the operator to assign the CpN(T), CpD(T)
functions
• Operator-dependent bias
• CpN(T) and CpD(T) functions typically are not refined
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• Are the CpN(T) and CpD(T) functions accurately modeled by
linear equations, constants or polynomials?
• CpN(T) appears to be reasonably well-modeled by a linear
function for many (but not necessarily all) proteins
• CpD(T) appears to have negative curvature for many proteins
• It may be possible to obtain CpD(T) over a broad
temperature regime by DSC in the presence of denaturant
• What are the characteristics of the instrumentation (vis a vis initial and
final datapoints)?
• We observe the greatest run-to-run variation for data within
the first few degrees (CpN(T)) and last few degrees (CpD(T))
• How much baseline data is necessary for accurate analysis?
• As much as possible (30° from Tm)
• Thermostable and unstable proteins are a problem
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Error of DCp(T) (CpD(T)-CpN(T)):
Tm
DCp(T) determines:
• DH(T)
• DS(T)
• DG(T)
The greatest accuracy in the
determination of all thermodynamic
parameters is at the Tm
Confidence wanes the further away we
move from the Tm
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Error and sample concentration…
• Data is normalized to a molar heat capacity, therefore, concentration
must be known
• What are the consequences of error in the sample concentration?
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Fit and residual looks like non2-state condition
(i.e. the presence of a folding
intermediate)
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Fit and residual looks 2-state
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Fit and residual looks like non2-state condition
(i.e. the presence of native state
oligomer)
Summary of concentration errors:
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• If the concentration is greater than you think:
• The fit will exhibit apparent non-2-state behavior N  I  D
• DHvH/DHcal < 1.0
• If the concentration is less than you think:
• The fit will exhibit apparent non-2-state behavior N2  2D
• DHvH/DHcal > 1.0
The basic take-home message:
Concentrations must be accurately known for DSC analysis!
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Cross-validation of DSC data
• DSC data collected in the presence of varying concentrations of added
denaturant can provide a 2-dimensional DGu profile (DGu versus T and [D])
• In principle, if we evaluate such a set of DSC data at a fixed temperature
(isotherm), we can predict DGu for isothermal equilibrium denaturation
• DGu as a function of denaturant can be derived from isothermal
protein folding studies, and compared to the predicted results from
DSC
• These values should agree if the assumptions of the model (and
concentrations) are correct
DGu Landscape as a function of temperature and denaturant from DSC data
20000
10000
0
-10000
DGu vs [D] isotherm
-20000
-30000
-40000
-50000
-60000
0.7
GuHCl (M)
0.8
0.9
1
1.1
280
1.2
290
300
310
320
330
340
-70000
350
Temp (K)
-1
D Gu (J mol )
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DGu = -RTln(Keq) = -RTln(ku/kf)
Human Fibroblast Growth Factor-1
Mutational effects upon stability
DDG @ Tm
of mutant
DDG @ Tm
of wild type
Tm
Tm
DDG = (DDG@Tm of wild type + DDG@Tm of mutant)/2