1. Theoretical physics, nanoscale protein dynamics, and neutrons
David J E Callaway

2. Overdamped, creeping motions
Protein motion—low Reynolds number
Overdamped, creeping motions
Badminton at bottom of swimming pool filled with molasses (low Re)
NOT
Titanic crossing Atlantic (high Re)
Theoretical physics is important! 2

3. Mobility tensor v = H F
H is the mobility tensor, and yields the velocity of a domain given the force applied on it or another subunit. NSE yields H, given structure.
(Bu et al, PNAS, 2005) 3

4. Effective diffusion constant measured by NSE can be easily calculated
(random coil cumulants of Akcasu and Gurol evolved by us into
theory of protein dynamics )
(L= Q x r )
ONLY inputs are D0 + structure + domain boundaries

5. for N identical domains connected by springs
We show by good old theoretical physics
Deff(Q→∞) = 2 x Deff(Q=0)
for a uniform rigid body, but can become as large as
Deff(Q→∞) = 2N x Deff(Q=0)
N = 2
for N identical domains connected by springs

6. NSE from Farago et al Biophys J 2010
NSE dynamics of (unbound) NHERF1 alone is well described by a rigid-body model
PDZ1
PDZ2 CT
NHERF1
NSE from Farago et al Biophys J 2010
Only inputs to calculations are diffusion constant and SANS coordinates—no need to fit NSE data or use MD! 6

7. Callaway et al, JMB 2017 A B Molecular nanomachinery! FERM EBD FERM
PDZ1
PDZ2
EBD B CT
EBD CT
FERM
PDZ1
PDZ2
Figure 1. Controllable activation of nanoscale dynamics in the disordered C-tail of NHERF1 alters binding kinetics to FERM. (A) Domain organization of NHERF1. The full-length protein consists of PDZ1, PDZ2, disordered C-terminal tail (CT), EBD (magenta), and S339/S340 (red). Shown is the activation of tip of whip motion in the phosphomimic mutant revealed by NSE. Structure model was generated using the NMR structures of PDZ1 (PDB code: xxx), PDZ2 (xxx), EBD (xxx), and SANS data using the program EOM (ref). (B) FERM (gold color) binding induces EBD (magenta) to adopt a helical conformation in the complex. The structure of EBD bound to FERM is from the crystal structure PDB code: 2d10 ref.XX. Structure model of the complex was generated using the known high-resolution domain structures, and SANS data. The graphics were generated using the program UCSF Chimera (ref).
Locate moving part
(frog tongue)
by NSE
Molecular nanomachinery! 7

8. A B C
Figure 4. NSE spectra as at different Q values for NHERF1(S339D/S340D) in (A) 150 mM NaCl, and (B) 150 mM NaCll, 20 mM dTris (pD=7.5) D2O buffer solution. (C) NSE measured Deff(Q) as a function of Q for NHERF1(S339D/S340D) in 300 mM NaCl (Black) and 150 mM NaCl (red), and 20 mM dTris (pD=7.5) D2O solution. Open black circle is the center-of-mass diffusion constant Do. The black lines are the Deff(Q) calculated from two sets of represented structural coordinates assuming rigid-body diffusion. The red lines are calculated Deff(Q) assuming motion near the “KRAP” motif. 8

9. NO large scale simulations or network models
Take-home message:
Can easily calculate Deff(Q) from:
structure + diffusion constant + domain boundaries
NO curve fitting
NO large scale simulations or network models
AND use it to characterize protein motion by NSE !
Theoretical (physics) approaches can be highly useful !

10. And a cast of hundreds from
ORNL
ILL
CCNY
Juelich
Stanford ….