protein simulationsdasher.wustl.edu/bio5357/lectures/lecture-13.pdfzimmerman and bowman. j chem...

Protein simulations

Greg Bowman

Molecular Dynamics

Molecular Dynamics

Sampling Challenge: Simulating Long Timescales is Extremely Hard

100

seconds 10-6

micro 10-15

femto 10-12

pico 10-9

nano 10-3

milli

Bond vibration

Isomer- ization

Water dynamics

Helix forms

Fast folding

Slow conf change

103

seconds

protein oligomerization

time on 1 fast CPU

3,000,000 years

~age of the

earth

3,000 years

3 years

1 day

long MD run

MD step

where we’d love to be

Bowman et al. Springer 2014.Knoverek et al. Trends Biochem Sci 2018.

Markov state models (MSMs) are quantitative maps of a protein’s energy

landscape

MSMs are Discrete-time Master Equation Models

!!(!)!! = !"!

! ! = !!"!(0)!

! ! = !!! !

!!!(!)!! = !!(!)×!!" − !!(!)×!!"

!!

Alanine Dipeptide: The State of the Art as of 2007

Chodera et al. JCP 2007.

The Villin Headpiece: The Unconquerable Frontier

Ensign et al. JMB 2007.Kubelka et al. JMB 2006.

A Simple Tutorial on Building MSMs

Dobson et al. Nature 2003.

Sampling with Stochastic Simulations

Clustering Gives a High-resolution Model

Clustering Gives a High-resolution Model

(This is a cartoon, since it’s hard to draw 10,000 states in a talk)

Clustering Gives a High-resolution Model

(This is a cartoon, since it’s hard to draw 10,000 states in a talk)

Lumping Provides Human Intuition

The Villin Headpiece: The Unconquerable Frontier

Bowman et al. JCP 2009.

Fre

e E

nerg

y (k

T)

native state prediction

MSM Retrodicts Native Structure and Folding Rate

Bowman et al. JCP 2009.

p(t+Δ&t)&=&T(Δ&t)p(t)&

Obs(t)&=&p(t)!Obs&

∆Gfold = -0.5 ± 0.5 kcal/mol

τfold = 1 (0.5, 5) μs

Testing for Two-state Behavior with Mean First Passage Times (MFPTs)Ui →N Ui →Uk

Bowman and Pande. PNAS 2010.

0.88 ± 0.27 μs 370 ± 220 μs

The Native State is a Kinetic Hub

Bowman and Pande. PNAS 2010.

The Unfolded Ensemble Brings Us Back to Levinthal’s Paradox

Bowman and Pande. PNAS 2010.

β-lactamase confers bacteria with antibiotic resistance

MSMs capture cryptic pockets

Pocketopening

Bowman and Geissler. PNAS 2012Bowman et al. PNAS 2015

Bowman. J Comput Chem 2016.Bowman et al. J Phys Chem B 2014.

Fluctuation amplification of specific traits (FAST)

Geometric observable of interest

Statistical uncertainty

Weighting factor

Start

Target

< < <Zimmerman and Bowman. J Chem Theory Comput 2015.

Zimmerman et al. J Chem Theory Comput 2018.

Pathways discovered by FAST-SASA

Zimmerman and Bowman. J Chem Theory Comput 2015.

Pathways discovered by FAST-SASA

Zimmerman and Bowman. J Chem Theory Comput 2015.

Pathways discovered by FAST-SASA

Zimmerman and Bowman. J Chem Theory Comput 2015.

Pathways discovered by FAST-SASA

Zimmerman and Bowman. J Chem Theory Comput 2015.

Pathways discovered by FAST-SASA

Zimmerman and Bowman. J Chem Theory Comput 2015.

Pathways discovered by FAST-SASA

Zimmerman and Bowman. J Chem Theory Comput 2015.

FAST outperforms conventional simulations and other adaptive schemes

Zimmerman and Bowman. J Chem Theory Comput 2015. Zimmerman… and Bowman. arXiv 2018.

FAST outperforms conventional simulations and other adaptive schemes

Zimmerman and Bowman. J Chem Theory Comput 2015. Zimmerman… and Bowman. arXiv 2018.

FAST outperforms conventional simulations and other adaptive schemes

Zimmerman and Bowman. J Chem Theory Comput 2015. Zimmerman… and Bowman. arXiv 2018.

FAST outperforms conventional simulations and other adaptive schemes

Zimmerman and Bowman. J Chem Theory Comput 2015. Zimmerman… and Bowman. J Chem Theory Comput 2018.