PowerPoint PresentationMolecular Models

Atomistic Models
() = =1
Atomistic models approximate QM with classical functions and Newtonian dynamics.
Why/when does it work? • Born-Oppenheimer approximation • No bond breaking/formation • No excited states • Moderate change in polarization
can be coupled with QM for regions where classical model is insufficient (e.g. enzyme active sites)
Bond Stretching
() = 2 − 0 2
Chemical type kbond lo C-C 100 kcal/mol/Å2 1.5 Å C=C 200 kcal/mol/Å2 1.3 Å C≡C 400 kcal/mol/Å2 1.2 Å
Bond distances are taken from crystallography (or QM), bond strength from spectroscopy. Similar term is used for bond angles.
= 1 2
potential
frequency
l
C=C 200 kcal/mol/Å2 1.3 Å
C≡C 400 kcal/mol/Å2 1.2 Å
Torsion Potential
θ
Torsion potential is implemented as cosine series with periodicity n and phase φ.
() =
Improper Torsions
= − 2
regular torsion
Non-bonded Interactions
TSTC 2019, Biophysics, Lecture I, Michael Feig
Non-bonded interactions are pairwise and applied to all pairs except 1-2 (bonds) or 1-3 (angles) pairs.
1-4 non-bonded interactions are often scaled (because of torsion terms).
() = =1
40
electrostatic interactions based on partial atomic charges fitted to match QM electric fields or interaction energies (with water)
() = =1
6
Lennard-Jones potential to model Pauli exclusion (typically r12) and van der Waals attraction (r6)
Coarse-Graining
TSTC 2019, Biophysics, Lecture I, Michael Feig
Coarse-graining refers to models that map atomistic models to lower resolution. Parameters are either determined from experiment (top down) or atomistic simulations (bottom up). Space (lattice models) and time (kinetic sampling algorithms) can also be coarse-grained.
Molecular Models

() = =1
united atoms
Reduced number of particles but retain physics as much as possible
Parameterization based on all-atom models.
All-atom-like interaction potential:
• Torsion potential fixes backbone secondary structure • Lennard-Jones interactions depend on particle type
(contact potential) • Electrostatic interactions only for charged sidechains
CG water model
CA
CO
SC1M
SC3M
Met side chain 3 CG vs. 11 AA atoms
Phe side chain 3 CG vs. 14 AA atoms
N
NCA
CO
SC2SC3
SC1
O
C
CB
CG
CD1CD2
CZ
CO
CA N
N
C
O
Cβ
This allows virtual sites to be generated on the fly to increase resolution without extra particles.
() = =1
TSTC 2019, Biophysics, Lecture I, Michael Feig
Additional empirical terms compensate for lack of resolution at CG level
N-CA-SC1L Angle
All-Atom Equivalence
All-atom energies can be matched directly. Simulations maintain all-atom accuracy without restraints.
Molecular Models

Residue/Shape-Level Coarse Graining
C-alpha
= − ln( )
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
0 1 2 3 4 5 6 7 8 9 10 11
en er
Elastic network (Go) models encode (non-local) native contacts (within structure and between molecules)
Internal conformation is kept via distance restraints or torsion terms.
helix extended
Inverse Boltzmann Method
TSTC 2019, Biophysics, Lecture I, Michael Feig
• Obtain PMFs for CG sites from simulations with all-atom force field
= =1
= − ln( ) • Fit harmonic/periodic terms to bonded PMFs
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 CA(2)-CA(3) distance in Å
PM F
en er
gy in
k ca
l/m ol
CA(2)-CA(5) distance in Å
PM F
en er
gy in
k ca
l/m ol
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
4 5 6 7 8 9 10 11 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
4 5 6 7 8 9 10 11
Force Matching
TSTC 2019, Biophysics, Lecture I, Michael Feig
Total pairwise forces from atomistic models are fit with effective CG forces (using spline functions).
This avoids issues with overlapping PMFs and overcounting entropy but model is highly system-dependent.
Protein Folding with Residue-Level CG Model
TSTC 2019, Biophysics, Lecture I, Michael Feig
Kolinski et al., Proteins, 18, 338 (1994) Protein folding within minutes on workstation!
B-Domain of Protein A (PDB ID: 1BDD)
Molecular Models

Colloid Models
Improved Colloid Models
embedded charges at sites of charged residues with screened electrostatics:
=
(,) = ε, − 1 2
TSTC 2019, Biophysics, Lecture I, Michael Feig
positive proteins tRNAs ribosomes other proteins
model of a bacterial cytoplasm
Multiscale Modeling
Different levels of resolution combine model accuracy with reduced cost
CG
AA
All-Atom
CG
Model with different resolutions in different parts of a system
Low- and high resolutions are switched
Resolution Mapping
Effective multi-scale methods require accurate mapping between resolutions.
High resolution low resolution is always easy. Low resolution high resolution is challenging!
All-atom CG
high/low energy
All-Atom Reconstruction from CG Models
>600 diverse proteins
TSTC 2019, Biophysics, Lecture I, Michael Feig
Atomistic-CG Hybrid Modeling
CHARMM + PRIMO
QM (active site)
Questions ?