Inferring protein structure and dynamics from simulation and experiment

...EVKMDAEFRHDS... ...EVKMDTEFRHDS... ...EVKMDVEFRHDS...

• Simulate the physical interactions of proteins in solution
• Numerically integrate the equations of motion

• Calculate experimental observables
• Generate atomic-detail hypotheses
• Interpret experimental observables

• Inferring Protein Dynamics from Molecular Simulation
• Quantitative Comparison of Villin Headpiece Simulations and Triple-Triplet Energy Transfer Experiments
• Inferring Conformational Ensembles from Noisy Experiments

• Run many parallel simulations on commodity hardware
• Build kinetic network model of dynamics
• Quantitatively predict structure, equilibrium, and kinetics

• Like FRET, but sensitive at the Å scale
• Used to monitor rates of contact formation

• Experimental advances revealed multi-state kinetics in smallest protein system
• MSMs capture multi-state kinetics and recapitulate TTET measurements
• Detailed comparison of simulation and experiment reveals need for better forcefields and observables

• Infer conformational ensembles from simulation and ambiguous experiments
• Simultaneously model structure and population
• Characterize posterior through MCMC
• Error bars on equilibrium and structural features

• Equilibrium molecular dynamics simulation, with conformations $x_j$
• Equilibrium experimental measurements $F_i$ with uncertainties $\sigma_i$
• Predicted experimental observables: $f_i(x)$

• Project onto basis of predicted experimental observables
• Reweight using a linear free energy: $-\sum_i \alpha_i f_i(x_j)$
• $\alpha_i$ tells how populations are perturbed by $i$th experiment

• Project onto basis of predicted experimental observables
• Reweight using a linear free energy: $-\sum_i \alpha_i f_i(x_j)$
• $\alpha_i$ tells how populations are perturbed by $i$th experiment

• Project onto basis of predicted experimental observables
• Reweight using a linear free energy: $-\sum_i \alpha_i f_i(x_j)$
• $\alpha_i$ tells how populations are perturbed by $i$th experiment

• Model for secondary structure / disorder peptides
• NMR Data: chemical shifts and scalar couplings

• Workhorse in protein folding, crystallography, and NMR

• Multiple disulfide (C14-C38) conformations in trypsin binding loop.

             X-Ray                          MD                              BELT

     $\frac{1}{n}\chi^2 = 15.0$          $\frac{1}{n}\chi^2 = 13.7$          $\frac{1}{n}\chi^2 = 10.4$

• BELT corrects forcefield bias in trialanine and BPTI
• Measure all scalar couplings for BPTI
• Better predictors of experimental observables: chemical shifts, scalar couplings, (TTET)
• Can we change the way NMR data is collected and analyzed?

• MSMs parallelize MD simulation, bringing millisecond-scale dynamics within reach
• Coupling MSMs to phenomenological model of TTET allows quantitative prediction of kinetic experiments
• BELT enables experiment-driven modeling of structure and equilibrium
• Open-Source Tools for protein inference (MSMBuilder, FitEnsemble)

• Pablo Cordero
• Frank Cochran
• Fang-Chieh Chou
• Parin Sripakdeevong
• Everyone!

Buzz Baldwin

Dan Herschlag

Pehr Harbury

Xuesong Shi

Laura Wang, Jessica Metzger, Aimee Garza, Crystal Spitale and all the Biochem staff

Kathleen Guan

Everyone!

Todd Martinez

Pehr

Russ Altman

Folding@Home Donors and Forum Volunteers (Bruce Borden)

OpenMM Team: Joy Ku, Peter Eastman, Mark Friedrichs, Yutong Zhao

Thomas Kiefhaber, John Chodera, Frank Noe, Jesus Izaguirre

DE Shaw Research

Susan Marqusee, Laura Rosen

$$P(i\rightarrow j, dark \rightarrow dark) = P_0(i\rightarrow j)$$ $$P(i\rightarrow j, dark \rightarrow light) = P_0(i\rightarrow j)$$ $$P(i\rightarrow j, light \rightarrow light) = (1 - f_i) P_0(i\rightarrow j)$$ $$P(i\rightarrow j, light \rightarrow dark) = \delta_{ij} f_i$$

• Structure + Equilibrium (not kinetics)
• Characterize the population of every conformation
• Rigorous connection to equilibrium measurements

Linear virtual biasing potential (LVBP): $\Delta U(x;\alpha) = \sum_i \alpha_i f_i(x)$

$\alpha_i$ tells how the energy of structure $x$ is changed by the predicted observable $f_i(x)$.

Populations by Boltzmann: $\pi_j(\alpha) \propto \exp[-\Delta U(x_j;\alpha)]$

The true ensemble is described by some coefficients $\alpha$.

Let $F_i$ be a noisy measurement of the $i$th experiment.

Let $\langle \rangle_\alpha$ denote an equilibrium expectation in the $\alpha$ ensemble.

$$P(F_i | \alpha) \approx N(\langle f_i(x)\rangle _\alpha, \sigma_i)$$

$$P(\alpha | F_1, ..., F_n) \propto P(F_1, ..., F_n | \alpha) P(\alpha)$$

$$\log P(\alpha| F_1, ..., F_n) = -\sum_j \frac{1}{2}\frac{(\langle f_j(x)\rangle _\alpha - F_j)^2}{\sigma_i^2} + \log P(\alpha)$$

MaxEnt prior: $\log P(\alpha) = \lambda \sum_i \pi_i(\alpha) \log \pi_i(\alpha)$

Use MCMC (pymc) to sample the likelihood function.