Biophysics 204

Part I - Calorimetry – ITCPart II - How to determine macromolecular size

23 Jan 2013

23 Jan 2013 Calorimetric Methods and Solution size determination

2

Thermodynamics

Define the Gibbs free energy of a system : G = H - TS

General expression for the change in free energy:

If ΔG < 0 the process is spontaneous.

The relation between free energy and an equilibrium constant.

van’t Hoff relation which tells us that the enthalpy of a reaction can be determined bymeasuring the equilibrium constant at a variety of temperatures:

Basic Thermodynamics of Protein Stability

Stability curve for a protein

Curvature comes from:

Tg and Tg’ are where ΔG=0Th and Ts are where ΔH and ΔS = 0

Relationship at temperature of maximal

stability. Note ΔH and ΔS are very steep

functions of temperature that arises from ΔCp. The range over which many proteins are maximally stable can belimited.

ΔCp - large and positive!

Range accessible by van’t Hoff

Protein Stability: The difference of two very large numbers.

Kinetic energyseparates atoms

Hydrophobicinteractions moststable

Hydrophobicinteractions weak

atoms closer together

Isothermal Calorimetry

• Maintain one temperature, and measure heat (Enthalpy change)

6

ITC

How does the experiment work?

Only method that can directlymeasure the binding energetics of biological processes

Isothermal Titration Calorimetry (ITC)

ΔH, contributions of individual interactions:van der Waals forces, (electrostatic, dipolar, hydrogen bonds – in non-aqueous environs) etc.

ΔS, Order changes: ΔSSOL, ΔSCONF, ΔSR,TR

Hydrophobic Interactions, Hydrogen bonds in aqueous environment Electrostatics in aqueous

Isothermal Titration Calorimetry (ITC)

Isothermal Titration Calorimetry (ITC) makes a direct measurement of the heat evolved or absorbed by the reaction that results from the mixing of two or more components.

We consider the simple binding reaction of a ligand (L) being introduced to a protein (P) to form a simple binary complex (PL). The heat evolution or absorption by this reaction is dependent on the enthalpy and the number of moles of complex formed.

For this equilibrium with the association constant Ka:

Where [L] is the unbound ligand concentration, [PT] is the total concentration of protein, [PT]= [P]+[PL], and [P] is the free protein.

Isothermal Titration Calorimetry (ITC)

Combining the equations that describe q and [PL] we get:

The way this is written we cannot get both ΔH and Ka from the same measurement (if we only measure q). In an actual experiment a fixed quantity of ligand added to a fixed amount of protein at defined intervals. For each interval the area under the peak can be integrated to give the total heat of the interval, qi.

There still are too many things we do not know here. What we do know if the total amount of ligand added [LT], or the ratio of, R = [LT]/ [PT]

Isothermal Titration Calorimetry (ITC)

We can fit this equation:

If we substitute the following:

Once Ka and ΔH0 are determined, ΔG0(T) can be calculated with:

And the entropy from:

ΔG =ΔH -ΤΔSSOL - TΔSCONF -ΔSR,TR

The ITC experiment

Illustration of ITC reaction cell (A), data (B), and analysis by non-linear regression (C)

ITC - heat-flux calorimeter - operates on the dynamic power compensation principle (i.e. how much power ∝cal/sec to keep the temperature between sample and reference cell constant)

ITC

What do real data look like?

Wintrode and Privalov, JMB 266 1050-1062 (1997)

An experiment with Calmodulin and a calmodulin binding peptide.

How could one determine ΔCp?

Why would looking at the temperature dependence be important?

15

Working c range: 1-1000

Best range for determination104 < Ka < 108

c = Ka[Mtot]n

ITC - Working range

c = 1

Ka = 104 M-1, [M]T= 100 μM

c = 10

Ka = 106 M-1, [M]T= 10 μM

c = 1000

Ka = 108 M-1, [M]T= 10 μM

Typical [M]T ~ 10 μM (Raising or lowering the solute concentration can push the range. Nevertheless this factor is going to be the major limit)

c = 1

c = 1

c = 10c = 10

c = 1000

c = 1000

ITC - Limits?

Some Kas may be too weak to get a good binding curve without using unobtainable amounts of reagent. The other limit is if the interaction is too tight (~ 1 nM). Here, each addition results in complete binding of ligand ([PL] ≈ [LT]. Since [P]=[PT]-[PL], when [LT] ≥ [PT], [P] ≈ 0 and the heat evolved will be zero. When [LT] < [PT], each titration will be exactly the same. This leads to a step function that cannot be fit accurately. 0.1 < Ka[M]T < 1000

ITCA way around the

problem of tight binders.

This reaction is too strong to measure accurately

Exploit a thermodynamic cycle to determine the tight binding ligand.

Sigurskjold (2000)

Example I:

Why is affinity reduced upon removing alpha 3?

What contributes to the entropy term?

Peptide binding imposes significant order in the delta 7ct case

Morrison equation

Specificity is coded in ΔH not ΔS

ΔH driven

DSC & ITC references

Becktel, W.J. & Schellman, J.A. ‘Protein Stability Curves’ Biopolymers 26:1859-1877 (1987)

Weber, P.C. & Salemme, F.R. ‘ Applications of calorimetric methods to drug discovery and the study of protein interactions’ Curr. Op. Struct. Biol. 13:115-121 (2003)

Velazquez-Campoy, A., Leavitt, S. A., & Freire, E. ‘Characterization of Protein-Protein interactions by Isothermal Titration Calorimetry’ Methods Mol. Biol. 261:35-54 (2004)

Velazquez-Campoy, A., & Freire, E. ‘ITC in the post-genomic era…? Priceless’ Methods Mol. Biol. 261:35-54 (2004)

Falconer, R.J., Penkova, A., Jelesarov, I., & Collins, B.M. ‘Survey of the year 2008: applications of isothermal titration calorimetry’ J. Mol. Rec. 23: 395-413 (2010) (contains general review plus ~ 500 references to ITC experiments covering protein/protein, peptide/protein, protein/drug. protein/lipid, protein/metal, protein/nucleic acid, nucleic acid/small molecule, etc. )

Sigurskjold, B.W. ‘Exact analysis of competition ligand binding by displacement isothermal titration calorimetry’ Anal. Biochem. 277: 260-266 (2000)

DSC & ITC references

Becktel, W.J. & Schellman, J.A. ‘Protein Stability Curves’ Biopolymers 26:1859-1877 (1987)

Weber, P.C. & Salemme, F.R. ‘ Applications of calorimetric methods to drug discovery and the study of protein interactions’ Curr. Op. Struct. Biol. 13:115-121 (2003)

Velazquez-Campoy, A., Leavitt, S. A., & Freire, E. ‘Characterization of Protein-Protein interactions by Isothermal Titration Calorimetry’ Methods Mol. Biol. 261:35-54 (2004)

Velazquez-Campoy, A., & Freire, E. ‘ITC in the post-genomic era…? Priceless’ Methods Mol. Biol. 261:35-54 (2004)

Falconer, R.J., Penkova, A., Jelesarov, I., & Collins, B.M. ‘Survey of the year 2008: applications of isothermal titration calorimetry’ J. Mol. Rec. 23: 395-413 (2010) (contains general review plus ~ 500 references to ITC experiments covering protein/protein, peptide/protein, protein/drug. protein/lipid, protein/metal, protein/nucleic acid, nucleic acid/small molecule, etc. )

Sigurskjold, B.W. ‘Exact analysis of competition ligand binding by displacement isothermal titration calorimetry’ Anal. Biochem. 277: 260-266 (2000)

Part II

How to measure molecular size

 

 

Part II How we measure macromolecular size? • Modern Detectors for ‘total Mass of

species’

• SAXS (Small Angle X-ray Scattering)

• (Mass Spectrometry for later in the course)

Growth in number and complexity of structures versus time

Macromolecular Structures

©Robert M. Stroud 2012

32

I. Molecular sieving methods 

 

The size of a protein molecule determines the rate of its passage through a molecular sieve. Molecular sieves consist of small particles of materials that have a network of pores into which molecules of less than some given maximum size can penetrate. (cf. continuous media such as a polyacrylamide gel).

Migration through the gel reflects the Stokes radius of the protein. In order to figure out the molecular weight of a test protein, one needs a set of molecular weight standards.  Test proteins may run anomalously if they are a very different shape from the standards (i.e. not spheres), or if they interact with the column.

35

SEC Tetra Detector Array (UV, LS, RI, IV) For the Purification and Characterization of Membrane

Proteins

Estimation of intrinsically disordered protein shape and time-averaged apparent hydration in native conditions by a combination of hydrodynamic methods Karst et al., Methods in Mol Biol 896 163-177 (2012)

CUV = UV/(KUV*dA/dc) Beer-Lambert LawCRI = RI* RIsol/(KRI*dn/dc) Snell’s LawMavg = KLS*Kopt*LS90º /(RIsol

2*C*(dn/dc) 2) Raleigh Equation for small molecules

(< 1/20 of λ670nm )Detector Calibration Response Factors Ks

Measured using stable protein with well known M, dn/dc and dA/dc

Shape and Size Detector (Differential Viscometer; measures Differential Pressure)IV= DP/C = dl/g (~~inversely α density)

Newtonian Viscosity (liquid layers) applied to tubes using Poiseulle’s Law

Vh = (M*IV)/2.5NA Einstein Vh for hard spheres = SEC Universal Calibration Principal Vh = 4/3*Rh

3π (volume of hydration)

Rh = [(3/10π)*IV*M/NA] ⅓

Tetra Detector Array/Analysis

Membrane Protein Expression Center © 2011

heterotrimer coexpressed and assembled in vivo and copurified crystallization and optimization of diffraction quality from 25Å to 3.2Å

Seleno-MAD/MR

Sec61αβγ

excessSec61β&γin micelles

SEC

Pascal Egea & Robert Stroud PNAS 2010

Crystal structure at 3.2Å resolutionof the Sec61αγ from Pyrococcus furiosus

Determine if Protein Detergent Complex can be concentrated before SECDictated by comparison of PDC and Micelle Retention Time

(Detergent/lipid RT measured for all common buffer-SEC systems)

Application

Superdex, 40mM OG TDAgram post 30kDa spin concentration

No

DP

RALS

RI

280nm

PDC

Excess OG micelle

RI inverted

DP

RALS

RI280nm

Excess OG micellePDC

YES

Superdex,40mM OG TDAgram post 40x 50kDa stir concentrate

PDC Homogenous tetramerGlobular (IV=0.05) with 5.7 nm RhBinds 260 OGContains 38mM excess OG in micelles0.17 dn/dc

Monomer

Dimer

Monomer

Tetramer

(AQP4)

SDX/2mM DDMPre S/2mM DDM 58x 50kDa stir

PDC 61mM DDM

280nmRI

RALS

DP

SDX/2mM DDMPost S at 9mg/ml

highermer PDC

-1.5mM excess DDM

S/2mM DDM

Minimize [detergent] during protein concentration using chromatographyE.g., Ion Exchange

Application

SDX/2mM DDMPost S & dialysis7.5mg/ml

280nmRI

RALS (90º)

DP

LALS (7º)

PDC

~0mM excess DDM

S/4mM DDM

Detergent minimized

Homogenous at high mg/ml

PHS+DF

MABi overlaid onto RI signal (5 Hz)

Large Center Peak Whole Peak Small Center Peak

10mg/ml  PDC MwMw/Mn

IVRh Wt Frac A Protein Mw

Monomers/PDC Moles DDM/PDC

All 386799 1.584 0.0389 5.516 0.190 73492 1.53 614Large 248260 1.007 0.0367 5.236 0.195 48411 1.03 391Small 244825 1.000 0.0355 5.159 0.198 48475 1.03 385

85% monodisperse (goal is >=95%)

Measuring Sample Homogeneity

TSK, 0.33mM DDM TDAgramMonomeric 12 crosserPost 25x 50kDa spin + mix

Application

N = 5  dimer/DDMMw (Da) IV (dl/g)

Rh (nm) Mp Mddmmoles

DDM/dimerAvg (sum/N) 290898 0.0336 5.37 157492 133406 220SD   1866 0.0011 0.06      

error in avg (relative error) SD/sqrt N 834 0.0005 0.03      

% avg error ((avg-pred)/pred)*100       18.94    % error in avg (absolute

error) (error in avg/avg)*100 0.29 1.42 0.47      

No excess micelles

Small errors in PDC Results

TSK, 1mM DDD TDAgram

PDC sample is P, H, S with Minimized Detergent!

Mw/Mn = 1.002 ± 0.0004 monodisperse

Mwi and RIheterodimer

8 Å, 1st attempt

Oligomeric State = 1.19 dimers/PDC

Multi-detector Copolymer UV Method

©Robert M. Stroud 2012 42

Can be applied tointrinsically ‘unfolded proteins’.

Solution scattering and shape of molecules

• Do not need crystals, but much lower Resolution

• Solution averages all orientations• Can see different populations in solution• Can determine overall shape of species• Can monitor time dependent conformation

change micro sec to days

©Robert M. Stroud 2012 43

©Robert M. Stroud 2012 44

©Robert M. Stroud 2012 45

©Robert M. Stroud 2012 46

©Robert M. Stroud 2012 47

©Robert M. Stroud 2012 48

SAXS determines accurate assembly state in solution, as shown for acetyl-CoA synthetase subunit Hura et al Nat Methods. 2009 August; 6(8): 606–612.

©Robert M. Stroud 2012 49

SAXS defines accurate shape and assembly in solution for unknown structures and can uncover unsuspected structural similarity. Experimental scattering curves for proteins with no known structural homolog (left, color) were compared with calculated scattering

©Robert M. Stroud 2012 50

Advances in X-ray scattering: from solution SAXS to achievements with coherent beams Javier Pe´ rez1 and Yoshinori Nishino2 Current Opinion in Structural Biology 2012,

Conceptual schematic of solution scattering with focused XFELs. Scattering patterns may lose circular symmetry when a small number of particles are illuminated with femtosecond pulses from XFELs. The angular fluctuations increase the amount of information in the scattering data and can be utilized for ab initio structure analysis of biomolecules in solution.