Biophysics 204 Part I - Calorimetry – ITC Part II - How to determine macromolecular size 23 Jan Jan 2013 Calorimetric Methods and Solution size determination

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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 by measuring 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=0 Th 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 be limited. ΔCp - large and positive! Range accessible by van’t Hoff

Protein Stability: The difference of two very large numbers. Kinetic energy separates atoms Hydrophobic interactions most stable Hydrophobic interactions 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 directly measure 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: ΔS SOL, ΔS CONF, ΔS R,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, [P T ] is the total concentration of protein, [P T ]= [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, q i. There still are too many things we do not know here. What we do know if the total amount of ligand added [L T ], or the ratio of, R = [L T ]/ [P T ]

Isothermal Titration Calorimetry (ITC) We can fit this equation: If we substitute the following: Once Ka and ΔH 0 are determined, ΔG 0 (T) can be calculated with: And the entropy from: ΔG =  ΔH -  ΔS SOL - TΔS CONF -  ΔS R,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 (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: Best range for determination 10 4 < K a < 10 8 c = K a [M tot ]n ITC - Working range c = 1 K a = 10 4 M -1, [M] T= 100 μM c = 10 K a = 10 6 M -1, [M] T= 10 μM c = 1000 K a = 10 8 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 = 10 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] ≈ [L T ]. Since [P]=[P T ]-[P L ], when [L T ] ≥ [P T ], [P] ≈ 0 and the heat evolved will be zero. When [L T ] < [P T ], each titration will be exactly the same. This leads to a step function that cannot be fit accurately. 0.1 < K a [M] T < 1000

ITC A 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: (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: (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: (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: (2000)

DSC & ITC references Becktel, W.J. & Schellman, J.A. ‘Protein Stability Curves’ Biopolymers 26: (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: (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: (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: (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

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 (2012)

C UV = UV/(K UV *dA/dc)Beer-Lambert Law C RI = RI* RI sol /(K RI *dn/dc) Snell’s Law M avg = K LS *K opt *LS 90º /(RI sol 2 *C*(dn/dc) 2 ) Raleigh Equation for small molecules (< 1/20 of λ 670nm ) 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 D ifferential P ressure ) IV = DP/C = dl/g (~~inversely α density) Newtonian Viscosity (liquid layers) applied to tubes using Poiseulle’s Law V h = (M*IV)/2.5N A Einstein Vh for hard spheres = SEC Universal Calibration Principal V h = 4/3*R h 3 π (volume of hydration) R h = [(3/10π)*IV*M/N A ] 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 excess Sec61β&γ in micelles SEC Pascal Egea & Robert Stroud PNAS 2010 Crystal structure at 3.2Å resolution of the Sec61αγ from Pyrococcus furiosus

Determine if P rotein D etergent C omplex can be concentrated before SEC Dictated 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 RI 280nm Excess OG micellePDC YES Superdex,40mM OG TDAgram post 40x 50kDa stir concentrate PDC Homogenous tetramer Globular (IV=0.05) with 5.7 nm Rh Binds 260 OG Contains 38mM excess OG in micelles 0.17 dn/dc Monomer Dimer Monomer Tetramer (AQP4)

SDX/2mM DDM Pre S/2mM DDM 58x 50kDa stir PDC 61mM DDM 280nm RI RALS DP SDX/2mM DDM Post S at 9mg/ml highermer PDC -1.5mM excess DDM S/2mM DDM Minimize [detergent] during protein concentration using chromatography E.g., Ion Exchange Application SDX/2mM DDM Post S & dialysis 7.5mg/ml 280nmRI RALS (90 º) DP LALS (7 º) PDC ~0mM excess DDM S/4mM DDM Detergent minimized Homogenous at high mg/ml PHS+DF

M ABi overlaid onto RI signal (5 Hz) Large Center PeakWhole PeakSmall Center Peak 10mg/ml PDC Mw Mw/Mn IV RhWt Frac AProtein MwMonomers/PDCMoles DDM/PDC All Large Small % monodisperse (goal is >=95%) Measuring Sample Homogeneity TSK, 0.33mM DDM TDAgram Monomeric 12 crosser Post 25x 50kDa spin + mix Application

N = 5 dimer/DDM Mw (Da)IV (dl/g) Rh (nm)MpMddmmoles DDM/dimer Avg (sum/N) SD error in avg (relative error) SD/sqrt N % avg error ((avg-pred)/pred)* % error in avg (absolute error) (error in avg/avg)* No excess micelles Small errors in PDC Results TSK, 1mM DDD TDAgram PDC sample is P, H, S with Minimized Detergent! Mw/Mn = ± monodisperse M wi and RI heterodimer 8 Å, 1 st attempt Oligomeric State = 1.19 dimers/PDC Multi-detector Copolymer UV Method

©Robert M. Stroud Can be applied to intrinsically ‘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

©Robert M. Stroud

©Robert M. Stroud

©Robert M. Stroud

©Robert M. Stroud

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

©Robert M. Stroud 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 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.