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TITAN: Two-dimensional lineshape analysis Chris Waudby Christodoulou Group c.waudby@ucl.ac.uk Andres Ramos Lisa Cabrita John Christodoulou Inhibition of fatty acid synthesis for treatment of tularemia OH Cl O Cl Cl OH O Cl OH O OH

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SLIDE 1

TITAN: Two-dimensional lineshape analysis

Chris Waudby

Christodoulou Group c.waudby@ucl.ac.uk Andres Ramos Lisa Cabrita John Christodoulou

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SLIDE 2

Inhibition of fatty acid synthesis for treatment of tularemia

O OH Cl Cl Cl O OH Cl O OH O OH

2

O OH

5

Inhibition of Francisella tularensis enoyl reductase (interaction of inhibitors with E–NAD+ complex)

Lu, H. et al. ACS Chem. Biol. 4, 221–231 (2009) Copeland, R. A. Nat Rev Drug Discov 15, 87–95 (2016)

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SLIDE 3

Inhibition of fatty acid synthesis for treatment of tularemia

O OH Cl Cl Cl O OH Cl O OH O OH

2

O OH

5

Lu, H. et al. ACS Chem. Biol. 4, 221–231 (2009) Copeland, R. A. Nat Rev Drug Discov 15, 87–95 (2016)

Survival (%)

100 80 60 40 20 1.0 1.5 2.0 2.5 3.0 0.5

Ki (nM)

a

In vivo . Lu et al. the relationship between the residence time of a series of Fabl enoyl‑reductase inhibitors and in vivo

  • activity. The plots presented here show the percent survival of mice 10 days after they were infected

Francisella tularensis and then treated with the inhibitors. Correlation of percent ). Correlation of percent survival with inhibitor residence

  • time. Figure is adapted with permission from

, Wiley.

slide-4
SLIDE 4

Inhibition of fatty acid synthesis for treatment of tularemia

O OH Cl Cl Cl O OH Cl O OH O OH

2

O OH

5

Lu, H. et al. ACS Chem. Biol. 4, 221–231 (2009) Copeland, R. A. Nat Rev Drug Discov 15, 87–95 (2016)

3.0

Survival (%)

100 80 60 40 20 160 140 120 100 80 60 40 20

Residence time (minutes)

b

In vivo . Lu et al. the relationship between the residence time of a series of Fabl enoyl‑reductase inhibitors and in vivo

  • activity. The plots presented here show the percent survival of mice 10 days after they were infected

Francisella tularensis and then treated with the inhibitors. Correlation of percent ). Correlation of percent survival with inhibitor residence

  • time. Figure is adapted with permission from

, Wiley.

Kinetics of ligand binding are crucial to in vivo activity

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SLIDE 5

Molecular mechanism of imatinib (Gleevec)

Agafonov, R. V., Wilson, C., Otten, R., Buosi, V. & Kern, D. Nat. Struct. Mol. Biol. 21, 848–853 (2014) Wilson, C. et al. Science 347, 882–886 (2015)

Mechanism of binding
 is central to activity

slide-6
SLIDE 6

∆ν

Rates of reactions and spectroscopic timescales

NMR UV frequency difference ∆ν ~ 1014 Hz kex ≪ ∆ν NMR frequency difference ∆ν ~ 100 Hz kex ≫ ∆ν UV ∆ν

http://casegroup.rutgers.edu/lnotes/NMR_lecture_dynamics.pdf

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SLIDE 7

100% A 100% B slow exchange

NMR lineshapes vs exchange rates

A ⌦ B

3 s–1 frequency difference 200 s–1

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SLIDE 8

100% A 100% B slow-intermediate exchange

NMR lineshapes vs exchange rates

A ⌦ B

30 s–1 frequency difference 200 s–1

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SLIDE 9

100% A 100% B fast-intermediate exchange

NMR lineshapes vs exchange rates

A ⌦ B

300 s–1 frequency difference 200 s–1

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SLIDE 10

100% A 100% B fast exchange

NMR lineshapes vs exchange rates

A ⌦ B

3000 s–1 frequency difference 200 s–1

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SLIDE 11

NMR lineshapes vs exchange rates

http://casegroup.rutgers.edu/lnotes/NMR_lecture_dynamics.pdf

magnetic field strength

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SLIDE 12

NMR titrations are information rich

structure (chemical shifts) molecular weight (linewidths) P PL ‡ free energy binding kinetics thermodynamics (∆G = RT ln Kd)

∆ν ~ 10 – 10,000 s–1 => measure exchange on timescales of µs – s

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SLIDE 13

NMR lineshape analysis

spin system parameters chemical shifts linewidths (relaxation rates) binding model parameters Kd, koff…

chemical shift ligand concentration

Bloch-McConnell equations

P + L ⌦ PL kex = koff + kon[L]

ligand concentration / µM 50 100 150 1 fraction bound chemical shift true fraction bound

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SLIDE 14

NMR lineshape analysis

spin system parameters chemical shifts linewidths (relaxation rates) binding model parameters Kd, koff…

chemical shift ligand concentration

Bloch-McConnell equations

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SLIDE 15

NMR lineshape analysis

example: ultrafast folding (10 µs timescale) of villin headpiece

Wang, M. et al. J. Am. Chem. Soc. 125, 6032–6033 (2003)

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SLIDE 16

From 1D to 2D…

1H chemical shift / ppm 15N chemical shift / ppm

7.0 7.5 8.0 8.5 7.0 7.5 8.0 8.5 108 110 112 114 116 108 110 112 114 116

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SLIDE 17

Lineshape analysis of 1D cross-sections

O'Connor, C. & Kovrigin, E. L. Biochemistry 51, 9638–9646 (2012)

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SLIDE 18

Why isn’t lineshape analysis more common?

  • Apathy – ‘Good enough’ to assume fast/slow exchange

and analyse chemical shift/intensity changes?

  • No! This risks systematic errors and ignores the

richness of titration datasets

  • Complexity of analysis?
  • Software needs to be easy to use!
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SLIDE 19

Problem #1: Peak overlap

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SLIDE 20

Problem #2: Normalisation

1H

1D pulse-acquire: 2D HSQC: signals decay during pulse program execution no delay between pulse and acquisition => signal proportional to concentration

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SLIDE 21

Problem #2: Normalisation

7.3 7.4 7.5 7.6 7.7

Raw intensities

7.3 7.4 7.5 7.6 7.7

1H chemical shift / ppm Normalised peak volumes

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SLIDE 22

Problem #2: Normalisation

7.3 7.4 7.5 7.6 7.7

Raw intensities

7.3 7.4 7.5 7.6 7.7

1H chemical shift / ppm Normalised peak volumes

7.3 7.4 7.5 7.6 7.7

Spectra with measurement noise

7.3 7.4 7.5 7.6 7.7

1H chemical shift / ppm Normalised peak volumes

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SLIDE 23

Problem #3: Differential relaxation

1H

1D pulse-acquire: 2D HSQC: signals decay during pulse program execution no delay between pulse and acquisition => signal proportional to concentration

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SLIDE 24

Problem #4: Multiple quantum evolution

7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117

1H chemical shift / ppm 1H chemical shift / ppm

HSQC HMQC

0 eq 0.25 eq 0.5 eq 0.75 eq 1 eq 2 s

– 1

2 s

– 1

2 s

– 1

2 s

– 1

ligand concentration dissociation rate [P]0 = 100 µM 700 MHz

ΔδH = 0.1 ppm ΔδN = 0 ppm

7.4 7.5 7.6 7.7

1H chemical shift / ppm

HMQC appears to have more binding than in HSQC

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SLIDE 25

There must be a better way! Existing methods – at best – analyse 2D data using 1D theory…

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SLIDE 26

Two-dimensional lineshape analysis

spin system parameters chemical shifts linewidths (relaxation rates) binding model parameters Kd, koff…

QM

7 7.5 8 114 115 116 117 114 115 116 117

1H chemical shift / ppm 15N chemical shift / ppm

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SLIDE 27

Two-dimensional lineshape analysis

spin system parameters chemical shifts linewidths (relaxation rates) binding model parameters Kd, koff…

QM

7 7.5 8 114 115 116 117 114 115 116 117

1H chemical shift / ppm 15N chemical shift / ppm

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SLIDE 28

Two-dimensional lineshape analysis

spin system parameters chemical shifts linewidths (relaxation rates) binding model parameters Kd, koff…

QM

pulse program +experimental settings +processing parameters

7 7.5 8 114 115 116 117 114 115 116 117

1H chemical shift / ppm 15N chemical shift / ppm

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SLIDE 29

Pulse programs / degrees of freedom

Evolution of isolated IS spin system (without chemical exchange): How many parameters can we expect to extract from a spectrum?

Helgstrand, M., Härd, T. & Allard, P. J. Biomol. NMR 18, 49–63 (2000)

16 free parameters!

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SLIDE 30

Two-dimensional lineshape analysis

Helgstrand, M., Härd, T. & Allard, P. J. Biomol. NMR 18, 49–63 (2000) Helgstrand, M. & Allard, P. J. Biomol. NMR 30, 71–80 (2004)

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SLIDE 31

Two-dimensional lineshape analysis

✓ No normalisation required between spectra ✓ Accounts for differential relaxation and MQ evolution

during pulse sequence

✓ Can avoid regions of peak


  • verlap or fit overlapping


signals simultaneously

8.4 8.5 8.6 8.7 120 120.5 121 121.5 122

1H chemical shift / ppm 15N chemical shift / ppm

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SLIDE 32

Example: FIR / Nbox interaction

FBP FUSE ssDNA GT rich RRM1 RRM2 Nbox FIR

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SLIDE 33

Lineshape analysis: FIR / FBP Nbox

  • bserved

fit

  • bserved

fit Kd = 14 ± 8 µM Kd = 22.7 ± 0.5 µM reported: fit: koff = 2700 ±100 s–1 RRM1 RRM2 Nbox FIR

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SLIDE 34

Lineshape analysis: FIR / FBP3 Nbox

Kd = 280 ± 36 µM Kd = 283 ± 2 µM reported: fit: koff = 15000 ± 300 s–1

  • bserved

fit RRM1 RRM2 Nbox3 FIR

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SLIDE 35

Global fit of 18 residues:

10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 10.7 10.8 10.9 11 11.1 121 121.5 122 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 8.8 9 9.2 114 115 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 9.3 9.4 9.5 115.5 116 116.5 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7.8 7.9 8 110 111 112 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 7 7.2 121 122 123 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.4 8.6 127.5 128 128.5 129 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.2 8.3 8.4 115 116 117 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.7 8.8 8.9 9 125 126 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.3 8.4 106 106.5 107 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 8.95 9 9.05 9.1 9.15 131.5 132 132.5 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 9.1 9.15 9.2 9.25 123 123.5 124 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126 7.9 8 8.1 125 125.5 126

slide-36
SLIDE 36

3D plots for inspecting goodness of fit

7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25 7 7.1 7.2 7.3 121 122 123 0.05 0.1 0.15 0.2 0.25

0 eq 0.1 eq 0.3 eq 0.6 eq 1.15 eq 1.7 eq 2.3 eq 2.9 eq 3.5 eq 4.6 eq 5.8 eq 6.9 eq 8.6 eq 11.5 eq 14.3 eq

  • bserved

fitted

slide-37
SLIDE 37

Example 2: TFP binding to (Ca2+)4-CaM

F S N N N F F

trifluoperazine

slide-38
SLIDE 38

8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

NMR titration

8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

slide-39
SLIDE 39

8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

Full binding model: 16 states, 32 equilibria

8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

slide-40
SLIDE 40

8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

Sequential binding model

8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68 8.4 8.6 8.8 9 123 124 125 126

1H chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

slide-41
SLIDE 41

2D lineshape fitting to sequential binding model

8.4 8.6 8.8 9 123 124 125 126 8.4 8.6 8.8 9 123 124 125 126

b

  • bserved

fitted

1H chemical shift / ppm 1H chemical shift / ppm 15N chemical shift / ppm 15N chemical shift / ppm

K115 F141 D118 D80 I63 S101 F68

c d e f

1 2 3 4 4 1 2 3 1 2 3 4

CaM 2270 ± 100 s-1 +TFP, 14 ± 1 μM CaM:TFP1 2070 ± 80 s-1 +TFP, 25 ± 1 μM CaM:TFP2 11000 ± 400 s-1 +TFP, 62 ± 2 μM CaM:TFP3 12000 ± 3000 s-1 +TFP, 4 ± 1 mM CaM:TFP4

a

based on global fit of 33 residues

slide-42
SLIDE 42

TITAN: Easy to use 2D analysis software

www.nmr-titan.com

slide-43
SLIDE 43

Use a variety of build-in binding models

www.nmr-titan.com

slide-44
SLIDE 44

Define regions of interest to avoid overlap

www.nmr-titan.com

slide-45
SLIDE 45

…or fit overlapping peaks directly

www.nmr-titan.com

slide-46
SLIDE 46

Check fit quality with 3D viewer

slide-47
SLIDE 47

Error analysis by block residual resampling (bootstrapping)

slide-48
SLIDE 48

Validation and comparison of simple and block resampling

−3 −2 −1 1 2 3 −10 −8 −6 −4 −2 2 4 6 8

Standard Normal Quantiles z-score QQ plot: parameter z-scores vs Standard Normal

Kd=1 μM, koff=5 s−1, σ=0.2

115 116

Kd=1 μM, koff=5 s−1, σ=0.5 Kd=100 μM, koff=5000 s−1, σ=0.5 Kd=10 μM, koff=500 s−1, σ=0.2

115 116

Kd=10 μM, koff=500 s−1, σ=0.1 Kd=100 μM, koff=5000 s−1, σ=0.1 Kd=1 μM, koff=5000 s−1, σ=0.5

7.5 7.6 115 116

Kd=1 μM, koff=500 s−1, σ=0.1

7.5 7.6

Kd=10 μM, koff=5000 s−1, σ=0.5

7.5 7.6

Simple bootstrap (N=1) Block bootstrap (N=5) simulate noisy synthetic data with parameters p0 fit data to estimate parameters, pfit calculate bootstrap error estimates, σ analyse distribution

  • f z-scores

z = (pfit – p0) / σ

1H chemical shift / ppm 15N chemical shift / ppm

Protein-ligand titrations were simulated with a fixed protein concentration of 50 µM and ligand concentrations of
 0, 12.5, 25, 50, 62.5 and 75 µM, with Kd varied between 1 and 100 µM and koff between 5 and 5000 s–1. The performance of the fitting algorithm was investigated with different levels of noise in the synthetic dataset.

slide-49
SLIDE 49

Exchange in HSQC vs HMQC spectra

7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117 7.5 7.6 116 117

1H chemical shift / ppm 1H chemical shift / ppm

HSQC HMQC

0 eq 0.25 eq 0.5 eq 0.75 eq 1 eq 2 s

– 1

2 s

– 1

2 s

– 1

2 s

– 1

ligand concentration dissociation rate [P]0 = 100 µM 700 MHz

ΔδH = 0.1 ppm ΔδN = 0 ppm

7.4 7.5 7.6 7.7

1H chemical shift / ppm

HMQC appears to have more binding than in HSQC

slide-50
SLIDE 50

Chemical exchange regimes

http://casegroup.rutgers.edu/lnotes/NMR_lecture_dynamics.pdf

magnetic field strength

ξ = ∆ω kex

Introduce the dimensionless parameter: Coalescence point (50:50 equilibrium)

ξ = √ 2 ξ p 2 ξ ⌧ p 2

Fast exchange Slow exchange

slide-51
SLIDE 51
  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

Chemical exchange regimes in 2D experiments: I-spin only

ξI = ∆ωI kex

ξS = ∆ωS kex

F S

∆ωobs =∆ωIpB Rex =∆ω2

I pApB

kex ∆ωobs =k2

expApB

∆ωI Rex =kAB

F S S

slide-52
SLIDE 52

Chemical exchange regimes in 2D experiments: HSQC

  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

ξI = ∆ωI kex

ξS = ∆ωS kex

F S S F S F S S

∆ωobs =k2

expApB

∆ωS Rex =kAB ∆ωobs =∆ωSpB Rex =∆ω2

SpApB

kex

slide-53
SLIDE 53
  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

Chemical exchange regimes in 2D experiments: HZQC

ξI = ∆ωI kex

ξS = ∆ωS kex

F S F S S

∆ωobs =(∆ωS − ∆ωI)pB Rex =(∆ωS − ∆ωI)2pApB kex

∆ωobs = k2

expApB

∆ωS − ∆ωI Rex =kAB

slide-54
SLIDE 54

∆ωobs = k2

expApB

∆ωS + ∆ωI Rex =kAB

∆ωobs =(∆ωS + ∆ωI)pB Rex =(∆ωS + ∆ωI)2pApB kex

  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

fast exchange (I-spin SQ) fast exchange (S-spin DQ)

Chemical exchange regimes in 2D experiments: HDQC

ξI = ∆ωI kex

ξS = ∆ωS kex

F S F S S

slide-55
SLIDE 55
  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

Chemical exchange regimes in 2D experiments: HMQC

ξI = ∆ωI kex

ξS = ∆ωS kex

SS– SS+ FF

∆ωobs =∆ωSpB Rex =(∆ω2

S + ∆ω2 I )pApB

kex

∆ωobs =k2

expApB∆ωS

∆ω2

S − ∆ω2 I

Rex =kAB

SZSD FZFD

Skrynnikov (2002)

slide-56
SLIDE 56
  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

Example: fast/fast exchange

∆ωobs =∆ωSpB Rex =(∆ω2

S + ∆ω2 I )pApB

kex

FZFD

  • 0.1

0.1 0.2 0.3 0.4 0.5 0.6

∆ δN / ppm

10 20 30 40 50 60 70 80 90 100

  • 0.1

0.1 0.2 0.3 0.4 0.5 0.6

∆ δN / ppm

10 20 30 40 50 60 70 80 90 100

MQ 15N lineshape SQ 15N lineshape kex 1000 s–1 ∆wN 200 s–1 ∆wH 200 s–1

slide-57
SLIDE 57
  • 0.5

0.5 1 1.5 2 2.5

∆ δN / ppm

10 20 30 40 50 60 70

MQ 15N lineshape

  • 0.5

0.5 1 1.5 2 2.5

∆ δN / ppm

10 20 30 40 50 60 70

SQ 15N lineshape kex 1000 s–1 ∆wN 1000 s–1 ∆wH 1750 s–1

  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

Example: slow/slow exchange SZSD

∆ωobs =k2

expApB∆ωS

∆ω2

S − ∆ω2 I

Rex =kAB

slide-58
SLIDE 58
  • 4
  • 2

2 4

  • 4
  • 2

2 4 ξI ξS

fast exchange (I-spin SQ) fast exchange (S-spin MQ)

MQ coalescence point

ξI = ∆ωI kex

ξS = ∆ωS kex

slide-59
SLIDE 59

Summary: 2D fast exchange regimes

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HSQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HMQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HZQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HDQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

SIM-H[Z/D]QC

slide-60
SLIDE 60

The SOFAST-SIM-H[Z/D]QC experiment

Separate HZQC and HDQC by post- acquisition receiver phase cycling Sensitivity – each experiment = 1/√2 of HSQC

1H 15N

Gz t1

decouple

g1 g2 g2

δ δ x,–x

500 1000 1500 2000 2500 3000 3500

Acquisition + recycle delay / ms

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Sensitivity

120 degree excitation 90 degree excitation

slide-61
SLIDE 61

The SIM-H[Z/D]QC experiment: cyclophilin

HZQC

1H chemical shift / ppm

7.0 8.0 9.0 10.0 90 100 110 120 130 140 150

HDQC

1H chemical shift / ppm

7.0 8.0 9.0 10.0 90 100 110 120 130 140 150

slide-62
SLIDE 62

Summary: 2D fast exchange regimes

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HSQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HMQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HZQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

HDQC

,

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 ξI ξS

SIM-H[Z/D]QC

slide-63
SLIDE 63

Paramagnetic longitudinal relaxation enhancement

Chan, Waudby et al. J Biomol NMR (2015) 63 151–163 Cai et al. JACS (2006) 128, 13474–13478

R1,p ≈ R2,p = 20S(S + 1)µ2

Bg2

15r6 γ2T1e

(T1e ⌧ τc)

δN / ppm SNRt / s-½

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.8 0.6 110 115 120 125

δH / ppm

Trec / s

7.0 7.5 8.0 8.5 1.0

δ δ

a b d

SNR / s

Δ

e

Δ [NiDO2A] / mM 20 40 60 80

40 mM NiDO2A 0 mM NiDO2A

slide-64
SLIDE 64

Summary

  • NMR titrations – a powerful tool for characterising structural,

mechanistic, thermodynamic and kinetic aspects of macromolecular interactions

  • Introduction of 2D lineshape analysis


– more accurate (differential relaxation, normalisation)
 – more convenient (peak overlap)
 – block residual resampling method for error analysis

  • Applications to simple ligand binding but also more complex models
  • Comparison of SQ, MQ, ZQ and DQ experiments provides

additional and complementary information on exchange phenomena

  • Download now for Mac and Linux! www.nmr-titan.com

Waudby, Ramos, Cabrita & Christodoulou. Sci Rep 6, 24826 (2016)