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

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

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

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

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

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

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

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

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 !

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