Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular

Dynamics

Introduction

S/WAXS

• SAXS: overall shape and size of the molecules
• WAXS: changes in tertiary and secondary structures
• Data interpretation is challenging.

MD simulations

• Atomic level details of molecular structures
• Sampling issue
• Force field bias

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SWAXS-driven MD

Foreknowledge

of

reaction paths

X

Theory: coupling potential

The coupling of the MD simulation to experimental target SWAXS curve

E_FF : energy from MD force field

E_SWAXS : energy penalty from disagreement

Quantifying the deviation between EXP and MD

I_c : computed SWAXS from simulations, on the fly

I_e : target SWAXS from experiment

n_q : intensity points

k_c : coupling strength/constant

Po-chia Chen and Jochen S. Hub, Biophysical Journal, 108, 25730-2584, (2015)

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Theory: calculation of SWAXS curves

Computed SWAXS scattering:

Fourier transforms of the instantons electron density of

the system A and B

Orientational average

Conformational average

Conformational average:

Envelope

Methods: on-the-fly calculation

N_A : atoms in envelop

f_i(q): atomic form factor

r_j : position of atom j

a_k , b_k , c_k: Cromer-Mann parameters

Methods: SWAXS-driven forces

Shannon sampling limit: q_maxD_max

Discussion: LBP

Red and green dots :

the ensembles of unbiased simulations of closed (red) and open (green) LBP

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Black dots:

Cluster center of closed and open ensembles used for the RMSD analysis in subplots (B and C)

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Orange/blue dots:

Conformations during SWAXS-driven MD in the opening (orange) and closing simulation (blue).

Orange and blue lines:

To guide the eye, smoothed SWAXS-driven trajectories are shown.

Black arrows:

Forces derived from E_SWAXS, mainly acting along the opening motion.

Discussion: LBP

• Scattering-curves of SWAXS-driven trajectories at t =10 ns, as compared to the target curves

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• The SWAXS curves and pair distribution functions P(r) computed from the final frames of the SWAXS-driven MD are in close agreement to the target curves

Thanks!