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Thermodynamic approaches to membranes and membrane interactions

Thermodynamic approaches to membranes and membrane interactions. Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk. Thermodynamic approaches to membranes and membrane interactions. thermodynamics ?. Thermodynamics.

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Thermodynamic approaches to membranes and membrane interactions

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  1. Thermodynamic approaches to membranes and membrane interactions Peter Westh NSM, Research Unit for Biomolecules Roskilde University pwesth@ruc.dk

  2. Thermodynamic approaches to membranes and membrane interactions thermodynamics ?

  3. Thermodynamics The science that deals with the relationship of heat and mechanical energy and the conversion of one into the other Webster’s New Universal Dictionary 1979 A branch of physics that studies …… systems at the macroscopic scale by analyzing the collective motion of their particles using statistics Wikipedia Jan. 2008 A macroscopic phenomenological discipline concerned with a description of the gross properties of systems Kirkwood & Oppenheim: Chemical Thermodynamics, 1961 Macroscopic – gross properties – heat and mechanical energy – statistics - phenomenological Relevance to molecular biology and biochemistry ?

  4. Thermodynamics and (bio)molecules • Department of molecular thermodynamics….. • Hydrogen bond thermodynamics. Calculation of local and molecular physicochemical descriptors ”HYBOT-PLUS” • Thermodynamics of protein folding (Cooper 1999) • Thermodynamics of membrane receptors and channels (MB Jacson 1993) How is that possible for an approach which is: ”phenomenological” “macroscopic” and describes “gross properties” ? Thermodynamics is your x-ray glasses which enables you to screen the models and mechanisms which are suggested to rationalize the exploding amount of empirical biochemical knowledge (functional and structural)

  5. Thermodynamics Is a wonderful structure with no contents Aharon Katchalsky For the (experimentally convenient) (P,T,ni) variable system Koga (2007) Solution Thermodynamics: a differential approach. Elsevier. For membranous (colloidal) systems perhaps a fourth variable: Area (dG/dA=g)

  6. Thermodynamic studies of membranes – a practical approach • Free energy of interaction • Calorimetry (energy of interaction): -scanning -titration -pressure perturbation -temperature modulated • Volumetric properties

  7. Measuring free energy (chemical potential) changes of interactions Two experimental approaches: • Direct (model free) Measures the equilibrium distribution. For example dialysis equilibrium, freezing point depression, membrane osmometry, liquid-liquid partitioning, vapor pressure (ion selective electrode) • Indirect (model based, DG°) Any technique (e.g. spectral, hydrodynamic, thermal) which quantifies the concentration of a species in a proposed reaction. For example protein folding UN , K=[N]/[U] and DG=-RTlnK Or membrane partitioning Peptide (aq)  peptide (membrane) Andersen et al (2005) J Biochem Biophys Methd50, 269.

  8. Free energy of interactionan example Water-phospholipid interactions (membrane hydration)

  9. Direct measurements of the water vapor pressure 30.0 23.5 18.4 Adsorption isotherm POPC 25C 14.5 Temperature scanning, DMPC-water. Pressure difference between moist lipid and pure water. Andersen et al (2005) J Biochem Biophys Methd50, 269.

  10. Faster methodsDynamic Vapor Sorption (DVS)

  11. Sorption calorimetry Heat (enthalpy) of adsorption is measured directly – the amount adsorbed is calculated from the evaporation enthalpy Bagger et al (2006) Eu. Biophys. J.35, 367.

  12. Sorption calorimetry DLPC 25C DMPC 27 C Sorption isotherm (net water affinity) Heat of sorption (DHw) Markova et al. (2000) J Phys Chem B104, 8052

  13. Lyotropic phase transitions DLPC DMPC Markova et al. (2000) J Phys Chem B104, 8052

  14. Calorimetry • We measure the temperature dependence of the free energy (Gibbs Helmholtz eq.) • Most often, this is not explicitly used – we quantify the course of a process through the heat it produces

  15. Membrane calorimetry • One of the oldest analytical principles still in use – Lavoisier had rather precise calorimeters by 1780. • Readily measured thermodynamic function. • Heat cannot be measured – temperature can. • Heat is NOT at state function – enthalpy and internal energy are.

  16. Modern instruments (ITC200) No water bath Noise level ~0.002mCal/sec or about 10nW. The heat capacity is about 3 J/K – detection level ~0.1mJ Hence the the thermal noise is about 1x10-7/3~3x10-8K !

  17. Two types of calorimeters have revolutionized biochemical applications • Differential Scanning Calorimetry (DSC) • Isothermal Titration Calorimetry (ITC)

  18. Classic use of DSC phase diagrams Blume (1983) Biochem. 22; 5436. Schrader et al (2002) J.Phys.Chem. 106, 6581 Böckman et al (2003) Biophys J.85, 1647

  19. DSC and the lever rule Binary membrane (two PCs) Phase diagram Schrader et al (2002) J.Phys.Chem. 106, 6581 The ratio nF/nG quantifies the conversion of gel to fluid phase and is hence reflected in the callorimetric heat flow

  20. Phase diagram for DOPE at low temperature and water content Derived – and remarkably complex – phase diagram Increasing water content DSC data Sharlev & Steponkus (1999) BBA1419, 229.

  21. Mixed membrane systemsPhase behavior of phospholipid-cholesterol systems 19 25 30 Temperature McMullen et al (1993) Biochem32, 516. DMPC/POPC + 28 % Cholesterol Luis Bagatolli http://scienceinyoureyes.memphys.sdu.dk

  22. Alcohols depress the main (Pb – La) phase transition temperature Pressure Increases Tm – Le chateliers principle!

  23. Alcohol and interdigitated phases Rowe & Cutera (1990) Biochem. 29, 10398

  24. Other compounds increase the main transition temperature Complex solute effects in Phosphatidyl enthanoamine KSCN Sucrose Koynova, et al. (1997) Europ. Biophys. J. 25, 261

  25. DH  0 → + Binding and PartitioningITC ”Foreign molecules” bind or partitioning into membranes We already saw the DSC approach to this – change in phase behavior reflects partitioning ! ITC approach – directly measure interaction: Basic idea!

  26. Technical overviewPower compensated ITC (after ~1990) The feed-back system sustains a constant and very small DT between cell and reference. Net refcell heat flow Exothermic process is compensated out by (fast) adjustment of the feed-back heaters. Electrical heater • +++ • Fast responce, high sensitivity • - - - • Narrow applicability, Feed-Back Control

  27. Simple approach Ligand in cell – titrate with membrane (NB the other way around won’t work since there is no saturation – it is partitioning between two phases) Lipid membrane; 47.4mM Octanol 0.61mM 1-octanol OcOH depletion Rowe et al (1998) Biochem. 37, 2430

  28. DH  0 → + ITC and partitioning:data analysis Partitioning scheme: A(aq) ↔ A(mem) Law of mass action: Kp=[Amem]/[Aaq] Mass conservation: [A]tot=[Amem]+[Aaq] Rowe et al. (1998) Biochem. 37; 2430.

  29. Weaker interaction requires more complex procedures Excess enthalpy, HE, of DMPC in 1-propanol HE is the enthalpic contribution of DMPC towards the total enthalpy of the system Hence, the slope HE/Calcohol is a measure of the enthalpy of DMPC-alcohol interactions Note that HE vs Calcohol is not linear. Trandum et al (1999) J.Phys.Chem.B103; 4751

  30. Interaction of ethanol and DMPCDependence of phase and cholesterol Phase behavior Interaction enthalpy And partitioning coefficient DMPC+10% Ganglioside Kp=87 DMPC+10% Sphingomyelin Kp=85 DMPC, Kp=28 DMPC+30% Cholesterol Kp=12 Partitioning of small alcohols scales with the membrane surface density DeYoung & Dill (1988) Biochem. 27, 5281. Cholesterol content Trandum et al (1999) BBA, 1420, 179 Trandum et al (1999) BBA1420; 179 Trandum et al (2000) Biophys J78; 2486

  31. Heat (and thus calorimetry) is the universal detector.Specialized methods show great versatility A ”release protocol” for the determination of membrane permeation rates 10mM POPC vesicles injected into 150mM C10EO7 (upper) and 1mM C10EO7+10mM POPC (lower) Heerklotz & Selig (2000) Biophys. J.81, 184.

  32. Another asset of calorimetry is high resolutionMicelle formation and protein surfactant interactions De-micellization of SDS CMC readily determined to within 10-50mM Otzen et al In press

  33. Another asset of calorimetry is high resolutionMicelle formation and protein surfactant interactions Andersen et al Langmuir in press

  34. A new generation of DSCTemperature Modulated DSC

  35. A linear gradient in T with a sine wave or zigzag superimposed Temperature Heat Flow

  36. In-phase and out-of-phase heat capacity single out different response/relaxation processes

  37. Pressure perturbation DSC Measures HEAT OF COMPRESSION Which is tantamount to THERMAL EXPANSIVITY

  38. PPC – two examples from biophysics Melting of egg sphingomyelin. Conventional DSC and PPC. DH=30.5 kJ/mol, DV=21 ml/mol Thermal denaturation of two globular proteins Area equals the volume change, DV, for the denaturation Heerklotz (2004) J. Phys Condens Matter16, R441

  39. Volumetric properties • V=dG/dp • Readily measured by vibrating tube densitometry. • ”Structural interpretation” and relationship to physical dimensions

  40. Vibrating tube densitometry Hollow quartz U-tube. Volume 1 ml Thermostatted 0.001 K Hook’s law Period measured to 1nsec Calibrate against air and water F~300Hz For liqiuds (and gasses): Specific volume (density) measured to within 10-6 to 10-5 cm3g-1 (g cm-3)

  41. Vibrating tube densitometry

  42. Volume (density) of pure membranes • DMPC @ 30C V~0.978 cm3/g (d~1.022 g/cm3) • DV @ Tm 4% • Monounsaturated PC membranes (e.g. both cis and trans DOPC) have higher volumes (~1.020 to 1.050 cm3/g @ 30C. • Polyunsaturated PC (like di-linolenoyl PC i.e. 18:3/18:3-cis-D9,12,15) have volumes similar to saturated PC Volume (density) of mixtures • Illustrates how the different species pack • May benchmark MD simulations Nagle & Wilkinson (1978) Biophys J 23, 159 Trandum & Westh (2000) J Phys Chem B 104, 11334

  43. Molecular packing:Experiment vs. simulation Voronoi assignments of molecular volumes DVhexanol (exp)= 4.2 ml/mol DVhexanol (exp)= 3.9 ml/mol

  44. Densitometry on membrane of membrane-solute systems A typical sample consists of 97% water 2.9% Phospholipid 0.1% fatty acid Measured specific volume V

  45. Molecular packing of alcohols in DMPC DV=Vapp-V (standard pure alcohol) Volume of each component Lipid alcohol water Aagaard et al 2005

  46. Closing Although thermodynamic functions reflects ”macroscopic properties” they effectly elucidate molecular aspects of membranes and membrane interactions. Calorimetry is the most precise and versatile experimental approach.

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