Recent Theory and Algorithms December 2, 2015 Predictive Multiscale - PowerPoint PPT Presentation

Coarse-Graining with the Relative Entropy: Recent Theory and Algorithms December 2, 2015 • Predictive Multiscale Materials Modeling • Cambridge, UK M. Scott Shell Department of Chemical Engineering University of California Santa Barbara Support Dreyfus Foundation National Science Foundation Avi Scott Chaimovich Carmichael

multi-peptide self assembly

Peptide self-assembled materials amyloid fibril nanotube nanowires dendrites 20  m gel nanospheres, vesicles plates, sheets flowers 5. Yan et al., Chem. Soc. Rev. (2010) 1. Tycko et al., Ann. Rev. of Phys. Chem. (2001) 2. Reches, et al. Science (2003) 6. Yan et al., Angewandte Chem. Int. Ed. (2007) 7. Govindaraju et al, Supramolec. Chem. (2011) 3. Amdursky et al, Biomacromolecules (2011) 8. Su et al, J. Mater. Chem. (2010) 4. Han et al, Colloids and Biosurfaces B (2011)

coarse-grained models of coarse-grained models of folding aggregation Zhang et al., J. Chem. Phys., 2009 Pellarin et al., J. Mol. Bio., 2006 HP lattice protein Lau & Dill, Macromol., 1989 bead-spring / Go-like Bellesia & Shea, J. Chem. Phys, 2007 Hall & coworkers, Proteins, 2010 Ueda et al, Biopolymers, 1978

information loss Shell, JCP (2008); Carmichael and Shell, JPCB (2012); Carmichael and Shell, JCP (2015)

Why coarse-grain? U CG all-atom configuration space coarse-grained configuration space fewer degrees of freedom, simpler interaction potentials, smoother energy landscapes, emergent physics/models

1 Basic motivation and theory for relative entropy coarse-graining 2 3 Other interesting properties 4 Future prospects for designing CG models

all-atom peptide model coarse-grained models of varying detail

Mapping (ALA) 15

Interactions ~225 total parameters

Equations of motion (optional)

A typical scenario in the CG’ing literature reference all-atom simulation / trajectory

Thinking instead about information loss

Thinking instead about information loss Shell, JCP (2008); Chaimovich and Shell, PRE (2010); Chaimovich and Shell, JCP (2011)

Example in one dimension... 0.45 0.45 all-atom all-atom 0.40 0.40 S rel = 0.38 S rel = 0.82 0.35 0.35 0.30 0.30 0.25 0.25 coarse- coarse- P(x) P(x) 0.20 0.20 grained grained 0.15 0.15 0.10 0.10 0.05 0.05 0.00 0.00 0 2 4 6 8 10 0 2 4 6 8 10 x x

Shell, JCP (2008); Chaimovich and Shell, PRE (2010); Chaimovich and Shell, JCP (2011)

1 Basic motivation and theory for relative entropy coarse-graining 2 3 Other interesting properties 4 Future prospects for designing CG models

relative entropy CG parameter space (potentials)

CG simulations reference all- every time atom parameters simulation change

perturb or reference all- “reweight” as atom parameters simulation change reference CG simulation regenerate if perturbation is too far away

No need for a new CG simulation at each iteration. Reweight the old one instead! Chaimovich and Shell, JCP (2011); Carmichael and Shell, JPCB (2012)

reference all-atom trajectory adaptive coarse-grained simulations model system: (ALA) 15

~80 total parameters Carmichael and Shell, JPCB (2012)

CG (ALA) 15

CG (ALA) 15

(AEAAKA) 4 9 bead types 81 potential terms

Shell, JCP (2008); Carmichael and Shell, JPCB (2012); Carmichael and Shell, JCP (2015)

Folding in bulk solution

Folding in bulk solution all-atom coarse-grained hairpin RMSD alpha helix coil helix R g

16 chains of (ALA) 15 (different colors) multi-peptide T = 300 K self assembly

16 chains of (ALA) 15 (different colors) multi-peptide T = 300 K self assembly

109.5° 109.5° all-atom water isotropic water

Lennard-Jones Gaussian (LJG) pair potential C. H. Cho, S. Singh, and G. W. Robinson, Phys. Rev. Lett. 76, 1651 (1996) 4 u(r) -2 1 3 r

D R 0.6 0.4 methanes PMF (kcal/mol) 0.2 0.0 -0.2 Shimizu & Chan (2000) -0.4 Czaplewski et al. (2005) -0.6 this work, CG water -0.8 3.0 5.0 7.0 9.0 R (Å) Hammer, Anderson, Chamovich, Shell, Israelachvili, Faraday Disc.(2010)

D R γ eff = Δ F min / A [mJ/m 2 ] 60 55 vs. 50 mJ/m 2 ≈ 55 in experiment 40 20 ≈ 79∙ D 0 0.0 0.4 0.8 1.2 1.6 D [nm] Chaimovich and Shell, JCP (2013).

1 Basic motivation and theory for relative entropy coarse-graining 2 3 Othe her r interesti teresting ng prope perties rties 4 Future prospects for designing CG models

What to match? (comparison to other CG metho Chaimovich and Shell, JCP (2011) see also: Rudzinski and Noid, JCP 135, 214101 (2011)

A. Chaimovich and M. S. Shell, Phys. Rev. E(2010); J. Chem. Phys. (2011).

atomistic coarse-grained 2D lattice gas, pairwise 2D lattice gas, mean-field • • • • ••• ••• ••• ••• • • • • errors in particle fluctuations | μ - μ c | [< n 0 n 1 > - < n > 2 ] err 0.10 0.0 0.2 nearest-neighbor 0.5 0.05 0.00 0.00 0.04 0.08 0.12 [< n 2 > - < n > 2 ] err 0.02 0.002 s rel / β bulk 0.01 0.000 0.00 0.00 0.04 0.08 0.12 s rel / β Chaimovich and Shell, J. Chem. Phys.(2011)

Useful for theoretical models too Shell, JCP (2012)

Fitting protein structure predictions to folding     2    E E D  ( ) exp 0  i i  p i  2 CG 2    E  E 0 configuration space distance ( D ) configuration space distance ( D ) Pritchard-Bell and Shell, Biophys J. (2011).

1 Basic motivation and theory for relative entropy coarse-graining 2 3 Other interesting properties 4 Future ture prospects spects for designing igning CG models dels

Mapping (ALA) 15

all-atom system coarse-grained hydrogens coarse-grained functional groups coarse-grained amino acid residues

The vast space of all possible CG models ln(# of CG models) 600 200 all-atom sites 500 150 400 ln S n, N 300 100 200 50 100 0 0 50 100 150 200 sites in CG model N

average probability of all AA configurations in the corresponding CG state

average AA energies within the CG state all of the complex ex stuff! f! • multibody interactions • temperature dependence Foley, Shell, Noid, J. Chem. Phys. (2015)

Case study: Gaussian Network Model “all - atom” 120 amino acid sites Foley, Shell, Noid, J. Chem. Phys. (2015)

Case study: Gaussian Network Model coarse-grained 12 pseudoatom sites Foley, Shell, Noid, J. Chem. Phys. (2015)

“intrinsic resolution” number of CG sites Foley, Shell, Noid, J. Chem. Phys. (2015)

“intrinsic resolution” number of CG sites Foley, Shell, Noid, J. Chem. Phys. (2015)

Summary The relative entropy provides a general statistical mechanical framework for coarse- graining that offers: theoretical insight into numerical methods bridges between intrinsic to create CG force various coarse- resolutions and fields graining optimal mappings strategies