Rosetta Energy Function Glenn Butterfoss. Rosetta Energy Function Major Classes: 1. Low resolution: Reduced atom representation Simple energy function

Rosetta Energy Function

Glenn Butterfoss


Major Classes:

1. Low resolution:

Reduced atom representation

Simple energy function

Aggressively search conformational space

2. High resolution:

Full atom

More sophisticated energy function

“Local” search of conformational (and sequence) space

Rosetta Energy FunctionLow resolution:

Atom Model

centroid reduction of side chains

Energy function terms

van der Waals repulsion

“pair” terms (electrostatics)

residue environment (prob of burial)

2º structure pairing terms (H-bonds)

radius of gyration

packing density

Implicit terms

fragments (local interactions)


Atom Model







radius of gyration

packing density

Implicit terms


In general …

Weighted linear combination

Energy = w1*term1 + w2*term2 + …

Pair-wise decomposable

Heavily trained on PDB statistics

Discriminate “near native” vs “non native”

No single low resolution score Several functions with different weights


χ1

χ2

Low resolution:

Atom Model







radius of gyration

packing density

Implicit terms



Atom Model







radius of gyration

packing density

Implicit terms


d

E

CLASH BAD!!

€

(rij2 − dij

2)2

r ijj<i

∑i

∑ ;dij < rij

€

d = distance

r = radii∑

Evaluate between Centoids and Backbone Atoms


Atom Model







radius of gyration

packing density

Implicit terms


Pair-wise probability based on PDB statistics(electrostatics)

€

−lnP(aai,aa j | sijdij )

P(aai | sijdij )P(aai | sijdij )

⎡

⎣ ⎢

⎤

⎦ ⎥

j>i

∑i

∑

aa = residue typed = centroid distance (binned, interpolated)s = sequence seperation (must be > 8 res )


Atom Model







radius of gyration

packing density

Implicit terms


neighbors within 10 Å of C

binned by : 0-3, 4,5, … , >30

also interpolated€

−ln P(aai | neighborsi)[ ]i

∑

Probability of burial /exposure(solvation)


Atom Model







radius of gyration

packing density

Implicit terms


Optimize 2º orientation


Atom Model







radius of gyration

packing density

Implicit terms


N

R1

R2

C

O

Represent protein as vectors of2 residue “strands”

sheet vector

helix vector


Atom Model







radius of gyration

packing density

Implicit terms


Coordinate system

v1

v2

r

hb

Scores selected to discriminate “near native structures for “non native”:

Relative direction ()

Relative H-bond orientation (hb)

Distance (r, r

Number of sheets given number of strands

Helix-Strand Packing


Atom Model







radius of gyration

packing density

Implicit terms


Used in earlier stages and for filtering€

RG = dij2

Density = −lnPcompact (neighborsi,sh )

Prandom (neighborsi,sh )

⎡

⎣ ⎢

⎤

⎦ ⎥

sh

∑i

∑

Promote a compact fold


Atom Model







radius of gyration

packing density

Implicit terms


LTSDELKAQWNTSTLVRHQEAGAS

set of non-redundantprotein structures

.

.

.


Atom Model







radius of gyration

packing density

Implicit terms


N C+

NC

Fragment insertion

Extended protein chain

NC

+

Select a site

Fragment insertion

Rosetta Energy FunctionHigh resolution:

Atom Model

full atom representation


Rotamer (Dunbrack)

Ramachandran

Solvation (Lazaridius Karplus)

Hydrogen bonding

Lennard-Jones

Pair (electrostatic)

Reference energies

In general …

Weighted linear combination

Energy = w1*term1 + w2*term2 + …

Pair-wise decomposable

Pre- tabulate energies

Hybrid Statistical / MM-like score

Weights trained for different applications


χ1

χ2

High resolution:

Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

experimental conformation

rotamer


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

rotamers


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

χ1

χ2

Dunbrack and Cohen library

€

−lnP(rotamer |φi,ψ i)P(aai |φi,ψ i)

P(aai)

⎡

⎣ ⎢

⎤

⎦ ⎥

i

∑

Based on PDB statistics

Backbone dependent

Additional rotamers from standard deviations of distributions


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

χ1

χ2

€

−ln P(φi,ψ i | aai,ssi)[ ]i

∑ss = secondary structure

Local backbone energy

Also used in some centroid refinement


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

Fast pair-wise additive

Penalize burial of polar residues

Simple solvation modelLazaridius Karplus

(standard)


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

Protein-DNA interactions: Generalized Born

Protein-Ligand: Coulomb

Simple solvation model(Special cases)


H

O

O

High resolution:

Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

Geometric H-bond potential

2 angles, 1 distance

Based on PDB statistics

r

H-bonding


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

r

CHARMM radii

Standard attractive potential

Repulsive term linearized

Note: command line options allow the repulsive term to be softened (radii reduced)

VDW interactions


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

Probability of finding residue types at give in distance

Defined by C coordinates

Electrostatics


Atom Model



Rotamer (Dunbrack)

Ramachandran


Hydrogen bonding

Lennard-Jones


Reference energies

Unique “cost” for designing in each residue type

G for bringing residue type into folded protein

Optimized with sequence recovery trials of folded protein structures

Correction for “folding”


Xavier

Rosetta CommunityThanks

Rosetta in Systems Biology

Structure Prediction:

Monte Carlo + Minimization search

p(E)?

Energy


Protein Design:

Protocol:

Packing:

Pre-tabulate table of all pair-wise rotamer energies

Monte Carlo search through rotamer / sequence space

With docking and backbone movement:

Iterate packing with (as above) with backbone / rigid body movements

Possibly apply restraints

docking, rmsd, disulfide, …


Protein Design:

Protocol:

Filtering:

Total energy

Packing quality

Avoid buried unsatisfied H-bonds(problem at interfaces)


Atom Model







radius of gyration

packing density

Implicit terms


€

−lnP aai,aa j | dij( )

P(aa

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

∑∑

Documents

Rosetta Energy Function Glenn Butterfoss. Rosetta Energy Function Major Classes: 1. Low resolution: Reduced atom representation Simple energy function