Molecular dynamics simulations allow researchers to model biomolecular mechanisms across wide ranges of time and length scales. The simulations integrate Newton's laws of motion over discrete timesteps to generate molecular trajectories. Force fields are used to define potential energies and forces in the system. While all-atom representation and applicability to diverse systems are advantages, the simulations are computationally expensive and limited in system size. The document provides examples of using molecular dynamics and small angle X-ray scattering to study protein folding, gene regulation, and protein structural ensembles.

1. Understanding Biomolecular
Mechanisms With Molecular
Dynamics Simulations
Jeff Wereszczynski
Illinois Institute of Technology
Department of Physics
Image Courtesy of David Goodsell

2. Biomolecular Dynamics Occur on a Wide Range of
Time and Length Scales
10-15
10-12
10-9
10-6
length scales (m)
timescales(s)
10-10
10-9
10-8
10-7
10-3
100
10-6
Side Chain Rotations
Loop Motions
Domain Motions
Protein Folding
Bond Motions

3. Computational Methods Have Been Developed that
Span that Range of Time and Length Scales

4. The “Force Field” Defines the Potential Energy
(and Forces) In a System
U r( )= Kr b − beq( )
2
bonds
∑ +
Kθ θ −θeq( )
2
angles
∑ +
Vn
2
1+ cos nφ −γ( )⎡⎣ ⎤⎦
dihedrals
∑ +
Aij
Rij
12
−
Bij
Rij
6
+
qiqj
εRij
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥i< j
∑
F r( )= −∇U r( )

5. In Molecular Dynamics (MD) Simulations, Newton’s
Second Law is Integrated Over Many Discrete Timesteps
Δt
calculate F(r)
Δt
calculate F(r)
Δt
calculate F(r)
Δt
calculate F(r)

6. Millions of Timesteps Create a Molecular Dynamics Trajectory
Advantages:
• All-atom
representation
• Can be applied to
diverse systems
• Can be used to
compute kinetic and
thermodynamic data
Disadvantages:
• Computationally
expensive
• Can be slow to
converge
• Limited system sizes
• Fixed-charged force
fields limits the
physics that can be
modeled

7. Running These Simulations
Anton 2
Traditional Clusters
GPUs

8. Molecular Basis for Gene Regulations
Tonna, El-Osta, Cooper, & Tikellis Nat. Rev. Nephr. (2010)
Morrison et al. (Under Review)

9. Small Angle X-Ray Scattering at BioCAT
• Located at the Advanced Photon Source
(APS), BioCAT is an NIH funded
research center dedicated to SAXS
• Comprises an undulator based beamline,
(18-ID) associated laboratory and
computational facilities.
• Available to all scientists on basis of
peer-reviewed beam time proposals

10. Determining Ensemble of Structures to Fit SAXS Data
Generate candidate structures
• aMD, cMD, Monte Carlo, TAMD, etc…
Pare down the structures into a
manageable number
• RMSD based clustering
Compute theoretical scattering
profiles for each structure
• Crysol (here), SasCalc, Capriqorn, etc.
Cluster scattering profiles
• χ2free based hierarchical clustering
Determine populations of states
• Bayesian Monte Carlo algorithm
χ2
free: Rambo & Tainer Nature (2013) X% Y%

11. Resisting Overfitting with Iterative Refinement to Find
Minimal Basis Set
1. Compute populations with
single scatterer
2. Compute each permutation of
two scatterer basis sets, take
the value with minimal χ2
3. Repeat N times until only all
scatterers in basis set
4. Choose ensemble size that
minimizes and the Akaike
information criterion (AIC)
AIC = 2k − 2ln L

12. Cluster Rg
(Å)
Distal
Group
Distance
(Å)
Interdomain
Angle
2 (54%) 32.6 ± 0.2 68.9 ± 0.4 120°±0.1°
9 (46%) 23.3 ± 0.3 41.0 ± 1.5 97°±8.3°
Combined 28.3 ± 0.3 ~ ~
Experiment 28.0 ± ~1.0 ~ ~
Iterative Refinement to Find Minimal Ensemble
0.00 0.05 0.10 0.15 0.20
q (
−1
)
10
-1
10
0
10
1
I[q]
0.00 0.05 0.10 0.15 0.20
q (
−1
)
10
-1
10
0
10
1
I[q]
Cluster 2
Cluster 9
2 9
Cluster No.
0.0
0.2
0.4
0.6
0.8
1.0
PopulationWeight
34.1
27.5
A
B
C
D
0.00 0.05 0.10 0.15 0.20
q (
−1
)
10
-1
10
0
10
1
I[q]
E

13. Conclusions & Future Directions
• Many tri-ubiquitin systems adopt both compact and
extended states in solution
• We are working to apply these methods to other systems.
• We are implementing these methods into “SASSIE”
Fig. 5. NMR structure model of an S. aureus tri-domain hemoglobin receptor, IsdHN2N3
. (a) The ensemble of the top 20
lowest-energy structures for IsdHN2N3
calculated using the two-step procedure outlined in Fig. 4 (steps 1 and 2). The
connector regions between each domain that were allowed to move during the conjoined rigid body/torsion angle
dynamics are colored red. Two views are shown related by a 180° rotation. (b) Ribbon diagram of the lowest-energy
structure of IsdHN2N3
. The N2, linker and N3 domains are colored green, yellow and blue, respectively. The residues
connecting the domains are colored red. Secondary structure elements are labeled for each subdomain. (c) Electrostatic
surface of IsdHN2N3
showing positively and negatively charged residues colored blue and red, respectively. (d) Graphical
summary of the PRE-derived distance restraint data used to determine the structure showing its compatibility with the NMR
structure. Data from probes providing attractive distance restraints are indicated by thick lines originating from spheres that
correspond to the backbone position of each probe: R363R1 (dark blue), E400R1 (yellow), E511R1 (red), K528R1 (pink),
1115PRE model ofIsdH Protein from Staphylococcus aureus
Fig. 5. NMR structure model of an S. aureus tri-domain hemoglobin receptor, IsdHN2N3
. (a) The ensemble of the to
N2N3
Variant Containing Nucleosomes: IsdH:
IsdH: Sjodt et al. J. Mol. Biol. (2016)

14. Acknowledgments
• Group Members:
• Dr. Stefania Evoli
• Dr. Emmanuel Naziga
• Dr. Francisco Rodriguez Ropero
• Samuel Bowerman
• Joseph Clayton
• Krystal Ma
• Amy Rice
• Dustin Woods
• Eve Venus
• Dr. Srinivas Chakravarthy (ANL)
• Funding:
• NIH: R15GM114758, R35GM119647
• NSF: MCB1552743, MCB1716099
• XSEDE Computing Resources