Biochemistry 675, Lecture 5 1. Enthalpy & Entropy: How can we [PDF]

Biochemistry 675, Lecture 5

1.  Enthalpy & Entropy: How can we experimentally determine these quantities?

2.  Molecular Interactions: Introduction







Noncovalent interactions







Water







Hydrogen Bonds

The Gibbs free energy for a process determines spontaneity

lnK = −

ΔG o ΔH o − TΔS o =− RT RT

•  ΔGo=ΔH-TΔSo

€ o •  and ΔG =-RTlnKeq,

•  When considering the structural basis of a favorable Gibbs free energy for a process one must take into account both the entropic and enthalpic driving forces.

•  Problem: If you rely only on determination of an equilibrium constant at a single set of conditions to determine the free energy you have learned nothing about the enthalpic and entropic driving forces for the process.

Fortunately we have Temperature and Van’t Hoff!!

•  dG=VdP-SdT









(1)

•  However, at constant pressure

•  dG=-SdT or (dG/dT)P=-S





(2)

•  Or (dG/dT)P=(G-H/T)







(3)

•  (d(G/T)/dT)P=1/T (dG/dT)P-(1/T2)G

(4)

•  Plug in equation (2) above

(d(G/T)/dT)P=-(TS+G)/T2





(5)

(d(G/T)/dT)P=-H/T2 GIBBS-HELMHOLTZ (6)



EQUATION-DOES NOT ASSUME THAT THE ENTHALPY CHANGE IS TEMPERATURE INDEPENDENT!!

Jacobus Henricus van 't Hoff 1901 Nobel Prize in Chemistry

http://nobelprize.org/nobel_prizes/chemistry/laureates/1901/hoff-bio.html

GIBBS-HELMHOLTZ

•  (d(ΔGo/T)/dT)P=-ΔHo/T2

•  Remember that ΔGo=-RTlnK

•  Measurement of the dependence of lnK/T on 1/T2 will provide information about the enthalpy of the reaction.

Van’t Hoff Analysis:Assume that the enthalpy change is T-independent

•  Start with Gibbs-Helmholtz

•  dlnK/dT=ΔH0/RT2

•  Integrate assuming that ΔH0 is constant:

T2

d lnK = ∫ ΔH o dT /RT 2 T1

ln

K 2 ΔH o 1 1 = ( − ) K1 R T1 T2

•  Measure the€ dependence of the lnK on 1/T-linear dependence with a slope of -ΔH0/R

Van’t Hoff Analysis

ln

K2 ΔH o 1 1 =− ( − ) K1 R T1 T2

€

Slope

9600 ± 532.9

Y-intercept when X=0.0 X-intercept when Y=0.0 1/slope

0.0001042

95% Confidence Intervals Slope

8230 to 10970

Y-intercept when X=0.0 X-intercept when Y=0.0 Goodness of Fit



r squared

0.9848

Sy.x

0.1646



-20.94 ± 1.822



0.002181







-25.62 to -16.25



0.001974 to 0.002336

•  Next: An example of application of the van’t Hoff analysis to binding of a “drug” to a protein

Binding of small molecules to an adaptive protein-protein interfaceMichelle R. Arkin,, Mike Randal, Warren L. DeLano､, Jennifer Hyde, Tinh N. Luong, Johan D. Oslob､, Darren R. Raphael､, Lisa Taylor, Jun Wang､, Robert S. McDowell､, James A. Wells, and Andrew C. Braisted Compound I

Arkin, Michelle R. et al. (2003) Proc. Natl. Acad. Sci. USA 100, 1603-1608

Structures of Compound1-Interleukin2 complex. Real structure

b.-d. Overlay of Cpd1 with Different Structures of IL2 Arkin, Michelle R. et al. (2003) Proc. Natl. Acad. Sci. USA 100, 1603-1608

Copyright ©2003 by the National Academy of Sciences

•  Conclusion from Structural Analysis

•  In the absence of ligand the protein has a range of conformations available to it. Upon binding of compound 1 the protein adapts to the ligand structure.

•  WHAT ABOUT THERMODYNAMICS?

Van’t Hoff analysis of Compound 1 binding to IL2

Arkin, Michelle R. et al. (2003) Proc. Natl. Acad. Sci. USA 100, 1603-1608

Copyright ©2003 by the National Academy of Sciences

•  Fig. 3.van't Hoff analysis of Compound 1 binding to IL-2. Kd values were determined at four temperatures

•  ΔHo=-8.90±.35kcal/mol,

•  ΔSo =-6.8±0.56cal/mol K.

•  Data are an average of three measurements; the standard deviations for each temperature are shown on the graph.

• Conclusions

• The binding is enthalpically driven. The

unfavorable entropy of binding, -TΔSo, is

consistent with the loss of configurational entropy by the protein upon binding of the ligand.

Enthalpy is temperaturedependent

•  Gibbs-Helmholtz

ΔGo = ΔH o (Tr )(1−

€

T T ) + ΔC p (T − Tr ) + T ln r Tr T

•  Tr is a temperature at which ΔHo and ΔCoP are known.

Alternatively: calorimetry

•  Use either Differential Scanning Calorimetry or Isothermal Titration Calorimetry to obtain the enthalpy for a

process directly as a function of temperature.

WE WILL SEE MORE CALORIMETRY!

Heat capacity

•  The heat capacity change at constant pressure can be obtained by measuring the temperature dependence of the enthalpy:

•  dΔHo/dT=ΔCp

•  We will see more of this in subsequent lectures.

Molecular Forces in Biological Interactions Multipe types of atomic level interactions must be considered in biological systems? These are primarily noncovalent.

•  •  •  •  •  • 

Hydrogen Bonding

Ion-Ion

Ion-Dipole

Dipole-dipole

Dipole-induced dipole

Induced dipole:induced dipole

All of these interactions occur in aqueous solution!

•  Water is a unique solvent! Its unique properties must be taken into account when considering the molecular basis of the energetics of biomolecular interactions.

http://www.britannica.com/eb/article-79421

Water has a large dipole moment.

Green-positive, Pink-negative http://www.lsbu.ac.uk/water/molecule.html

Hydrogen bonding of 2 water molecules

http://www.lsbu.ac.uk/water/molecule.html

Solid and liquid water are characterized by extensive Networks of hydrogen bonds

Hydrogen bonds between" water molecules are " diagramatically represented" by the black lines. The red" lines are covalent bonds " that hold oxygen (red) and" hydrogen (blue) atoms" together in the water " molecules."

Density of Water

T /K

Density g/mL

D2O

273

0.999841

1.10469

274

0.999900

275

0.999941

276

0.999965

277

0.999973

1.1057

278

0.999965

1.10562

279

0.999941

280

0.999902

281

0.999849

282

0.999781

281

0.999700

Water becomes less dense Upon freezing.

Electric Dipole Moment" of Some Gas Molecules" Molecule "m /D" NaCl " "9.0" KCl " "10.3" CO " "0.1" HF " "1.8" HCl " "1.1" HBr " "0.8" H 2O " "1.8" SO2 " "1.6" N2O " "0.2" "1.5" NH3 "

Water is very polar

Ions in aqueous media are surrounded By waters of hydration.

What is the energy of hydration? Enthalpy of hydration, Hhyd, of an ion is the amount of energy released when a mole of the ion dissolves in a large amount of water forming an infinitely dilute solution in the process, Mz+(g) + mH2O

Mz+(aq) where Mz+(aq) represents ions surrounded by water molecules and dispersed in the solution. The approximate hydration energies of some typical ions are listed on the next slide. The table illustrates the point that as the atomic numbers increases, so do the ionic sizes, leading to a decrease in absolute values of enthalpy of hydration.

Enthalpy of Hydration (ΔHhyd kJ/mol) of Some Typical Ions Ion ΔHhyd Ion ΔHhyd Ion ΔHhyd H+ -1130 Al3+ -4665 Fe3+ -4430 -Li+ -520 Be2+ -2494 F-505 Na+ -406 Mg2+ -1921 Cl-363 K+ -322 Ca2+ -1577 Br-336 + 2+ Rb -297 Sr -1443 I -295 Cs+ -276 Ba2+ -1305 ClO4-238 -Cr2+ -1904 Mn2+ -1841 Fe2+ -1946 Co2+ -1996 Ni2+ -2105 Cu2+ -2100 2+ 2+ 2+ Zn -2046 Cd -1807 Hg -1824

If hydration energies are so favorable, sequestering of a charged group in a biological interface will be energetically costly in terms of stripping water molecules away from the charged group.. www.science.uwaterloo.ca/~cchieh/cact/applychem/ waterphys.html

Enthalpy of Hydration (ΔHhyd kJ/mol) of Some Typical Ions Ion ΔHhyd Ion ΔHhyd Ion ΔHhyd H+ -1130 Al3+ -4665 Fe3+ -4430 -Li+ -520 Be2+ -2494 F-505 Na+ -406 Mg2+ -1921 Cl-363 K+ -322 Ca2+ -1577 Br-336 + 2+ Rb -297 Sr -1443 I -295 Cs+ -276 Ba2+ -1305 ClO4-238 -Cr2+ -1904 Mn2+ -1841 Fe2+ -1946 Co2+ -1996 Ni2+ -2105 Cu2+ -2100 2+ 2+ 2+ Zn -2046 Cd -1807 Hg -1824

If hydration energies are so favorable sequestering of a charged group in a biological interface will be energetically costly in terms of stripping water molecules away from the charged group.. www.science.uwaterloo.ca/~cchieh/cact/applychem/ waterphys.html

Water has a very large enthalpy of vaporization!

hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

Hydrogen Bonds in Biomolecular Interactions

Klotz& Franzen (1962) JACS, 84, 3461-3466

Klotz& Farnham (1968) Biochemistry, 7, 3879-3882

Baldwin, R.L. (2003) J. Biol.Chem. 278, 17581-17588.

Folding: For a typical 100 amino acid polypeptide 70

backbone hydrogen bonds are predicted to form upon folding

Hydrogen bonding in an α-helix and a β -sheet. (From Voet&Voet, Biochemistry, 1990, John Wiley.)

Binding: Many protein ligand complexes involve formation

of hydrogen bonds between the protein and the ligand

Complex of the biotin ligase (BirA) with biotinol-5’-AMP.

The green dashed lines are hydrogen bonds

Question: Given the preponderance of hydrogen bonding at

a structural level, how much do they contribute to the energetics of biomolecular processes?

History

The concept of the Hydrogen Bond was first introduced by M.L. Huggins in 1919 while still a student at UC Berkeley.

He referred to it as a Hydrogen Bridge

Different Hydrogen Bonds

H-bond geometries,

PNAS Morozov et al. 101 (18): 6946.