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

• M. Scott Shell

Department of Chemical Engineering University of California Santa Barbara Support Dreyfus Foundation National Science Foundation

Coarse-Graining with the Relative Entropy: Recent Theory and Algorithms

December 2, 2015 • Predictive Multiscale Materials Modeling • Cambridge, UK

Avi Chaimovich Scott Carmichael

multi-peptide self assembly

• 1. Tycko et al., Ann. Rev. of Phys. Chem. (2001)
• 2. Reches, et al. Science (2003)
• 3. Amdursky et al, Biomacromolecules (2011)
• 4. Han et al, Colloids and Biosurfaces B (2011)

amyloid fibril nanotube nanospheres, vesicles gel

20 m

nanowires plates, sheets flowers dendrites

• 5. Yan et al., Chem. Soc. Rev. (2010)
• 6. Yan et al., Angewandte Chem. Int. Ed. (2007)
• 7. Govindaraju et al, Supramolec. Chem. (2011)
• 8. Su et al, J. Mater. Chem. (2010)

Peptide self-assembled materials

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

coarse-grained models of folding coarse-grained models of aggregation

information loss

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

Why coarse-grain?

all-atom configuration space coarse-grained configuration space UCG fewer degrees of freedom, simpler interaction potentials, smoother energy landscapes, emergent physics/models

Basic motivation and theory for relative entropy coarse-graining

1 2

Future prospects for designing CG models

4

Other interesting properties

3

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

(ALA)15

Mapping

~225 total parameters

Interactions

Equations of motion (optional)

reference all-atom simulation / trajectory

A typical scenario in the CG’ing literature

Thinking instead about information loss

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

Thinking instead about information loss

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 2 4 6 8 10 P(x) x

Srel = 0.82

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 2 4 6 8 10 P(x) x

Srel = 0.38

Example in one dimension...

all-atom all-atom coarse- grained coarse- grained

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

Basic motivation and theory for relative entropy coarse-graining

1 2

Future prospects for designing CG models

4

Other interesting properties

3

CG parameter space (potentials) relative entropy

reference all- atom simulation CG simulations every time parameters change

reference all- atom simulation perturb or “reweight” as parameters 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

Carmichael and Shell, JPCB (2012)

~80 total parameters

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

all-atom coarse-grained RMSDalpha helix Rg

Folding in bulk solution

helix hairpin coil

16 chains of (ALA)15 (different colors) T = 300 K

multi-peptide self assembly

16 chains of (ALA)15 (different colors) T = 300 K

multi-peptide self assembly

isotropic water all-atom water

109.5° 109.5°

• 2

u(r) r

Lennard-Jones Gaussian (LJG) pair potential

• C. H. Cho, S. Singh, and G. W. Robinson, Phys. Rev. Lett. 76, 1651 (1996)

D R

Hammer, Anderson, Chamovich, Shell, Israelachvili, Faraday Disc.(2010)

• 0.8
• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 0.6 3.0 5.0 7.0 9.0 PMF (kcal/mol) R (Å) Shimizu & Chan (2000) Czaplewski et al. (2005) this work, CG water

methanes

55 vs. 50 mJ/m2 in experiment

20 40 60 0.0 0.4 0.8 1.2 1.6 γeff = ΔFmin / A [mJ/m2] D [nm] ≈ 79∙D ≈ 55

D R

Chaimovich and Shell, JCP (2013).

Basic motivation and theory for relative entropy coarse-graining

1 2

Future prospects for designing CG models

4

Othe her r interesti teresting ng prope perties rties

3

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).

0.00 0.05 0.10 0.00 0.04 0.08 0.12 [<n0n1>-<n>2]err srel/β 0.0 0.2 0.5 |μ-μc| 0.00 0.01 0.02 0.00 0.04 0.08 0.12 [<n2>-<n>2]err srel/β 0.000 0.002

errors in particle fluctuations nearest-neighbor bulk

• •
• •

atomistic 2D lattice gas, pairwise coarse-grained 2D lattice gas, mean-field

• •
• •

Chaimovich and Shell, J. Chem. Phys.(2011)

Useful for theoretical models too

Shell, JCP (2012)

configuration space distance (D) E configuration space distance (D)

 E0 

Pritchard-Bell and Shell, Biophys J. (2011).

 

        

2 2

2 exp ) (  

i i CG

D E E i p

Fitting protein structure predictions to folding

Basic motivation and theory for relative entropy coarse-graining

1 2

Future ture prospects spects for designing igning CG models dels

4

Other interesting properties

3

(ALA)15

Mapping

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

The vast space of all possible CG models

50 100 150 200 100 200 300 400 500 600

N

ln S n, N

ln(# of CG models) sites in CG model

200 all-atom sites 150 100 50

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)

Foley, Shell, Noid, J. Chem. Phys. (2015)

“all-atom” 120 amino acid sites

Case study: Gaussian Network Model

Foley, Shell, Noid, J. Chem. Phys. (2015)

coarse-grained 12 pseudoatom sites

Case study: Gaussian Network Model

number of CG sites

Foley, Shell, Noid, J. Chem. Phys. (2015) “intrinsic resolution”

number of CG sites

Foley, Shell, Noid, J. Chem. Phys. (2015) “intrinsic resolution”

The relative entropy provides a general statistical mechanical framework for coarse- graining that offers:

Summary

numerical methods to create CG force fields theoretical bridges between various coarse- graining strategies insight into intrinsic resolutions and

• ptimal mappings