Free energy, electrostatics, and the hydrophobic e ff ect Magnus - - PowerPoint PPT Presentation

▶
free energy electrostatics and the hydrophobic e ff ect
SMART_READER_LITE
LIVE PREVIEW

Free energy, electrostatics, and the hydrophobic e ff ect Magnus - - PowerPoint PPT Presentation

Feb 02, 2024 438 likes •886 views

Protein Physics 2016 Lecture 3, January 26 Free energy, electrostatics, and the hydrophobic e ff ect Magnus Andersson magnus.andersson@scilifelab.se Theoretical & Computational Biophysics Recap Protein structure Electrostatics

slide-1
SLIDE 1

Free energy, electrostatics, and the hydrophobic effect

Protein Physics 2016 Lecture 3, January 26

Magnus Andersson

magnus.andersson@scilifelab.se Theoretical & Computational Biophysics
slide-2
SLIDE 2

Recap

  • Protein structure
  • Electrostatics & hydrogen bonds
  • Van der Waals / Lennard-Jones
  • Interaction strengths
  • Energy Landscapes
  • The Boltzmann Distribution
  • Free Energy and entropy
slide-3
SLIDE 3

To sum up last week

  • Two critical results:
  • Protein folding is about
conformations

  • f long polypeptide chains - how can
it fjnd the best structure?
  • Reaction directions are determined
by free energy; F=E-TS. 
 Stable states are F minima.
slide-4
SLIDE 4

Outline today

  • Hydrophobic effect revisited
  • Connection to F = E - TS
  • Connection to protein folding
  • Strength of electrostatics in proteins
  • Titratable amino acid side chains
slide-5
SLIDE 5

Water Phase Transitions

  • Systems wants to stay at lowest F
  • ICE: Low E, low low S
  • Water: Higher E, higher S
  • When temperature is low, fjrst term (E) 

dominates F=E-TS
  • When temperature is high, second
term
 (TS) dominates F=E-TS
  • Can we use this to understand
slide-6
SLIDE 6 Gain: Energy of 1 h-bond (EH<0) Loss: Entropy of 1 (0.5*2) freely rotating water (SH>0) Vacuo Water
slide-7
SLIDE 7

Peer challenge

Which is true for H-bond formation at room temperature?

A) EH < TSH B) TSH < EH

Don’t forget the sign!
slide-8
SLIDE 8

FH= EH - TSH

slide-9
SLIDE 9

H-bond ΔG for proteins

D D A A In vacuo ΔG? D D A A In solvent ΔG? State A State B
slide-10
SLIDE 10 Why do some molecules like oil/gas better? Why do some molecules like water better?
slide-11
SLIDE 11

Partitioning

  • Consider transfer of hydrocarbon to H2O
  • Concentrations (X) rather than
probability
  • Count per mol, so we use R instead of k
  • X∝exp{-G/RT}
  • ∆Gliq->aq = -RT ln (Xaq/Xliq)
slide-12
SLIDE 12

9.25 mol/l 0.0001 mol/l

ΔGliq➝aq=+6.7kcal/mol

slide-13
SLIDE 13

Hydrocarbon transfer

  • ∆Gliq->aq=+6.7 kcal/mol at room temp
  • Not spontaneous process
  • It costs free energy to solvate hexane in H2O
  • Why?


G= H - TS

slide-14
SLIDE 14

ΔH? ΔS? ΔG?

ΔG= ΔH - TΔS

slide-15
SLIDE 15

Thermodynamic T

  • Minor perturbations at equlibrium
  • F+dF = 0 F + dE - TdS - SdT = 0
  • At equilibrium under constant V & T, 

this leads to:
 dF=dE-TdS=0
  • or: T = dE/dS
  • This was the thermodynamic defjnition 

  • f temperature that we covered last week

slide-16
SLIDE 16

S vs. Temperature

  • dF=d(E-TS)=dE-TdS-SdT
  • at equilibrium, dE-TdS=0 (last slide)
  • Thus, at constant volume we get:

S=-dF/dT
  • And at constant pressure it is S=-dG/dT
  • Compare T = dE/dS from last slide
  • This solves our problem!
  • Measure G at multiple T to get S!
slide-17
SLIDE 17

Hydrophobic solvation

We can compare 
 the gas phase with
 aqueous or liquid 
 phases the same 
 way! Knowing ΔG(T), we can calculate the other properties!
slide-18
SLIDE 18

Hydrophobic effect

Clathrate structures

ΔH? ΔS? ΔG?

Can you account for these processes?
slide-19
SLIDE 19

Temperature dependence

  • Strong dependence for H
  • Strong dependence for
TS
  • G is a small difference!
slide-20
SLIDE 20

Thermodynamic data

∆G virtually proportional to area!
slide-21
SLIDE 21

Accessible surface area

Probe radius 1.4Å “Solvent accessible surface area”
slide-22
SLIDE 22

Amino acid area

  • For amino acids, we get

very good agreement if
 we remove ~50Å2 per
 polar atom!

slide-23
SLIDE 23

Hardening of structure

  • What happens after hydrophobic collapse?
Once we have a separate
 hydrophobic phase, the cost
 is very low to “harden” it,

  • r even form a crystal
What does this mean for proteins?
slide-24
SLIDE 24
slide-25
SLIDE 25
slide-26
SLIDE 26

What about proteins?

  • Folding moves
hydrophobic residues from water to liquid/ interior phase
  • Opposite process to
solvation, so we
 use the opposite sign
  • or....
  • Flip the plots!
slide-27
SLIDE 27

Protein stability

Free energy of ‘unfolding’ Free energy of ‘folding’ (fmipped y axis) Solvate hydrocarbon in water, like we did earlier Going from water to hydrocarbon, which is the opposite process
slide-28
SLIDE 28

ΔG of Protein Folding

90% Hydrophobic effect 10% “Polishing” (Van der Waals packing)

slide-29
SLIDE 29

Electrostatics

  • So, hydrogen bonds are important
  • Governed by electrostatics
  • V=q1q2/εr
  • What is ε for us?
slide-30
SLIDE 30

Cost of forming charge

protein
slide-31
SLIDE 31

Charged amino acids

‘Titratable’
slide-32
SLIDE 32

Charges in protein

  • It costs roughly 40kcal to introduce a

unit charge in a protein (ε=3)!
  • Compare to ~1.5kcal in water (ε=80)
  • In practice, charges are rare inside 

proteins
  • Titratable amino acids typically
uncharged instead.
slide-33
SLIDE 33

Compare

Hydrogen bonds? kT? (thermal energy) Stability of a protein?

slide-34
SLIDE 34

What is ε in a protein?

slide-35
SLIDE 35

Screening of charges

slide-36
SLIDE 36

Electrostatics Permittivity, Ɛ

(farads/m)

Jens Erik Nielsen, JACS, 2013 Brian Mazzeo, JPCB, 2011
slide-37
SLIDE 37

Electrostatics on the atomic level +

  • V=q1q2/ε0r

Vacuo

slide-38
SLIDE 38

In a medium

slide-39
SLIDE 39

And even closer...

ε?

slide-40
SLIDE 40

What is ε in the last slide?

A) ε ≅1 B) ε ≅3-4 C) ε ≅20 D) ε ≅40-80 100 kcal/mol 30 kcal/mol 6 kcal/mol 1.5 kcal/mol

slide-41
SLIDE 41

Salt solubility in water

Energy between two charges at 3Å with ε=80: 1.5kcal/mol Compare with hydrogen bonds!
slide-42
SLIDE 42

Summary

  • Protein folding is largely determined

by hydrophobicity
  • Hydrophobic effect
  • Applications of enthalpy, entropy
  • Free Energy of processes
  • Protein folding, “molten globule”
  • Electrostatics in water is mostly entropy!
  • Chapters 5 & 6 in the Protein Physics book