Literature Seminar:
Bridging Theory & Experiment with Metainference — a Bayesian Inference Approach
Robert M. Raddi
(Advisor: Dr. Vincent Voelz)
Tuesday, Nov 12th, 2019
4:00 pm in BE 162
Determining biological structures requires a combination of experiment and theory
Solving structures with NMR:
Experimental
Computational:
References
Bayesian inference is the logical framework for combining separate sources of information
Laws of conditional probability
Combination of events:
The joint probability of some conformation X and experimental data D is P(X,D)=P(X)P(D), where X and D are independent.
Conditional Probability:
Suppose we want to know how the outcome of some conformation X is influenced by some experimental data D. Now the probability of some conformation X and experimental data D is
P(X,D)=P(X|D)P(D)
=P(D|X)P(X)
Bayes' Theorem:
P(X|D)= P(D|X)P(X)P(D)
Bayesian inference of structured ensembles
The likelihood function P(D|X) is related to the experimental restraints (how well does X agree with D)
The prior P(X) is the estimate of the probability before the data.
The posterior probability P(X|D) is a function of some hypothesis (what we want to know).
P(D) is the marginal likelihood is the same for all possible hypotheses. We treat as a normalization factor.
Incorporating errors:
Nuisance parameter σ, which could be chemical shifts, NOE distances, etc...
Posterior Distribution⏞P(X,σ|D)∝Likelihood⏞PExp(D|X,σ)Prior⏞PSim(X)NuisanceParameter⏞P(σ)
...this is how we make inferences in the face of uncertainty...
Posterior distribution can be sampled by Markov Chain Monte Carlo (MCMC)
Protocol for MCMC:
1. Start at some point X, σ. Compute P(X,σ).
2. Roll dice and draw a new point X∗, σ∗. Compute P(X∗,σ∗).
3. Accept move with probability Paccept if: Paccept=min(1,P(X∗,σ∗)P(X,σ)), then set X, σ = X∗, σ∗.
Ensemble of replicas of the system solves the problem of ensemble averaged data
Testing Metainference with a well defined system—Ubiquitin
Ubiquitin — NMR structure (PDB: 1D3Z)
Modeling:
- Chemical Shifts: CA, CB, CO, HA, HN, NH
- RDC (set 1): NH, CAC, CAHA, CN, CH
Validation: (back-calculation of the Exp. data not used in modeling)
- Scalar Coupling: 3JHNC, 3JHNHA
- RDC (set 2): NH
- RDC (set 3): NH, CAC, CAHA, CN, CH
The Metainference ensemble supports previous findings
A known source of dynamics involves a flip of the backbone consisting of Aspartic acid—D52 and Glycine—G53.
The flip is coupled with the formation of a H-bond (β state) between the backbone of Glycine—G53 and side chain of Glutamic acid—E24
Validation
Summary
- Metainference algorithm combines experimental and theoretical models to infer conformational ensembles
- Bayesian inference is used for combining all sources of information to deal with uncertainty
- MI was applied to a classic system & method validation supports MI
Future directions
- Bayesian inference can be used to improve force fields in MD simulations
- Metadynamic Metainference - time-dependent bias potential acting on selected CVs
Thank You for listening : )
Voelz Lab — Halloween 2019
From left to right: Shahlo Solieva, Si Zhang, Vincent Voelz, Tim Marshall,
Steven Goold, Yunhui Ge, Robert Raddi, Dylan Novack, Matthew Hurley,
Lei Qian
Additional thanks to:
Dr. Wunder & classmates
