Beckstein Lab Computational Biophysics at Arizona State University - PowerPoint PPT Presentation

Beckstein Lab Computational Biophysics at Arizona State University Hydrodynamics beyond Navier-Stokes: Nanofluidic transport through the lens of the numerical model Sean L. Seyler † , Charles E. Seyler ‡ , Oliver Beckstein † † Department of Physics, Center for Biological Physics, Arizona State University ‡ School of Electrical and Computer Engineering, Cornell University Blue Waters Symposium June 3, 2019

Structure-function connection

Structure-function connection extracellular Transport intracellular

What about the solvent bath? Timescales of interest: micro- to milliseconds+

Fully atomistic simulations are really expensive Billions to trillions of steps Timesteps: Timescales of interest: femtoseconds micro- to milliseconds+

Can a hybrid atomistic-continuum approach help? • All-atom MD in restricted subdomain … • Fluctuating HydroDynamics (FHD) for surrounding solvent hydro FH MD B MD I. Korotkin, el at. J. Chem. Phys. 143 (2015). G. De Fabritiis, et al. PRL 97 (2006)

Hydrodynamics is relevant at shorter length scales than expected Velocity fi eld (magnitude): 2D turbulence extracellular fl uid intracellular fl uid (cytosol)

Top-down view Hydrodynamics is relevant at shorter length scales than expected 90° Velocity fi eld (magnitude): 2D turbulence Streamlines: planar lipid membrane † † M. Chavent et al. Faraday Discussions 169 , 455 (2014)

Hydrodynamic equation in conservation form ∂ t φ + r · ( φ u ) = S ( φ ) Mass ∂ t ρ + r · ( ρ u ) = 0 φ − → ρ Momentum ⇢ uu + p ~ ⇣ ⌘ I + ~ ~ φ − → ρ u @ t ( ⇢ u ) + r · = 0 ~ � Energy h i u ( E + p ) + u · ~ @ t E + r · = 0 ~ � φ − → E Stress-strain ⟹ Navier-Stokes (Newtonian fluid) ✓ ◆ r u + ( r u ) T − 2 3( r · u ) ~ ~ ~ � = − ⌘ ~ I

Hydrodynamic equation in conservation form Account for thermal fluctuations in stress ∂ t φ + r · ( φ u ) = S ( φ ) and heat flux (not shown) † Mass ∂ t ρ + r · ( ρ u ) = 0 φ − → ρ Momentum ⇢ uu + p~ ⇢ uu + p ~ � + ~ ⇣ ⇣ ⌘ ⌘ I + ~ I + ~ ~ ~ ~ φ − → ρ u @ t ( ⇢ u ) + r · = 0 @ t ( ⇢ u ) + r · = 0 ~ ~ � S Energy � + ~ h h i �i u ( E + p ) + u · ~ � ~ ~ @ t E + r · @ t E + r · u ( E + p ) + u · = 0 = 0 ~ � ~ φ − → E S Stress-strain ⟹ Navier-Stokes (Newtonian fluid) ✓ ◆ r u + ( r u ) T − 2 3( r · u ) ~ ~ ~ � = − ⌘ ~ I † L. D. Landau & E. M. Lifschitz, Fluid Mechanics , third ed. (1966).

Hydrodynamic instabilities show that fluctuations matter ~ 100 nm Landau-Lifschitz Navier-Stokes Navier-Stokes velocity

Nanojet breakup: snapshots in time 100 nm NS 100 nm FHD 0 ns 8 ns 12 ns 16 ns 20 ns time