essential dynamics of proteins using geometrical
TRANSCRIPT
Essential Dynamics of Proteins using Geometrical Simulation
with Subspace Analysis
Presentation of Doctoral Dissertation by Charles Christian David
PREVIEW The BIG PICTURE
Why BCB Loves Proteins
• Proteins are central to cellular function, i.e., LIFE
• We hope to uncover the secrets of how these complex macromolecules execute their functions
• The dream is to 'watch' proteins in action: in real time at atomic resolution
• We approach the dream with our models.
Dynamic Trajectory of Myoglobin
DISSERTATION PROJECT Overview of the research
Three Phases I. Benchmark the Geometrical Simulation
Model (GSM)
II. Compare GSM results to molecular dynamics (MD) and elastic network model (ENM)
III. Apply the GSM to myosin V
INTRODUCTION Overview of Essential Dynamics & PCA
Essential Dynamics (ED)
• The process of applying Principal Component Analysis (PCA) to a protein trajectory
PCA A General Overview
PCA I • Identifies directions of
highest variance in data
• A standard method of data compression and dimension reduction
• The analysis is done on a centered C-Matrix (C): – Covariance matric (Q) – Correlation matrix (R)
PCA II • An eigenvalue decomposition is performed on C • The eigenvalues are plotted on a “scree plot” – Scree Plots help identify the Essential Subspace
PCA III • The primary limitations of PCA: – Linear Transform – Second Moment – Orthogonal – Quality of Data Sampling
• PCA is not limited to Cartesian DOF – Internal Distance Coordinates è dPCA
PCA IV • Major advantage of ED is choice of subset – Examine the large-scale motions within the subset of
residues – Under the influence of the entire set of residues
contained in the protein • Active sites • Potential allosteric pathways
Principal Component Analysis: A Method for Determining the Essential Dynamics of Proteins. Charles C. David and Donald J. Jacobs [Submitted July, 2012]
PART I Benchmarking the GSM
GEOMETRICAL MODEL Overview of the paradigm
GSM I
• An all atom, athermal, mechanical model
• Geometrical Constraints used to define rigid regions of the input structure
• Molecularly realistic perturbation of those rigid regions yields conformers (Monte Carlo)
GSM II
• FIRST Floppy Inclusions and Rigid Substructure Topology – Covalent Bonds – Hydrogen Bonds (HB) (pseudo temp) – Hydrophobic Tethers (HP Tethers)
• Recasts the protein into a set of rigid regions joined by hinges – Rigid Cluster Decomposition (RCD)
GSM III • FRODA
Framework Rigidity Optimized Dynamics Algorithm – MC sampling of perturbations to the RCD
– Molecular “realism” is enforced in FRODA • Constraint violations à Reject Conformer
– Two general modes of operation: • Diffusion (random) • Momentum (biased)
Methods I
• We obtained the FIRST/FRODA implementation of the GSM from the Thorpe Group at ASU
Generating stereochemically acceptable protein pathways. Farrell, D.W., Kirill, S., Thorpe, M.F. Proteins, 78, 2908-2921. 2010
• We designed a Java software package for the ED analysis of dynamic trajectories
Essential Dynamics of Proteins with Subspace Analysis in Java. Charles C. David and Donald J. Jacobs [In Preparation]
Methods II
• We assessed the behavior of the model for: – Effectiveness – Efficiency – Consistency
SUBSPACE METRICS Assessing Similarity of Essential Spaces
Subspace Metrics I • Overlap:
• Cumulative Overlap:
• Root Mean Square Inner Product:
• Principal Component Projections:
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Subspace Metrics II • Principal Angles – An optimization that gives the best alignment
between the two subspaces – Reveals timescales of dynamic congruency
VS DIM = 3 SS DIM = 2 2 PAs
Results I
• FRODA yields trajectories very quickly
• The trajectories equilibrate rapidly when using the momentum perturbation (MP)
Conformation RMSD
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Results II • Momentum bias is very effective
Figure 2.1 Conformation RMSD using FRODA Diffusion mode.!Running FRODA in diffusion mode yields trajectories that do not equilibrate rapidly due to low efficiency in how configuration space is sampled. These results are for MV in rigor state, which contains 946 residues.!
Results III • Output frequency can be optimized – For most proteins: 10 ≤ FREQ ≤ 50
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Figure 2.2 The dependency of equilibration rate on output frequency.!There is a trade-off between sampling every conformation and sampling every 100th conformation. Here, the conformational RMSD is plotted as a function of FRODA output, with the abscissa showing conformations from 1 to 2,000. Using an output frequency of 25 to 50 balances the time needed to sample more of the configuration space with the requirement to achieve sufficient statistical sampling. These results are for myoglobin, which contains 151 residues.!
Results IV • Constraint violations are minimized by: – Step Size ≤ 0.01Å when using MP
Results V • Configuration space is well sampled based on
the projections onto the top two PC modes
Results VI • Dependency on model parameters
PDB ID 2nwd: Structure of chemically synthesized human lysozyme at 1 Angstrom resolution
Results VII • There is a great degree of similarity in the essential
spaces over a wide range of parameter choices – This suggests a Range of Physicality
• Amplitude vs. correlation in the motion
Conclusions • The GSM is very fast and yields trajectories that equilibrate
rapidly when using the MP • The simulations did not become irrevocably jammed nor
did they yield structures containing large constraint violations
• Sampling of the native basin is efficient as assessed by
projecting the DVs on the top few PCA modes • The Essential Mode Spaces are highly conserved over a
wide range of constraint assignment parameters as measured by RMSIP and PA – A Range of Physicality was observed
• The GSM well characterizes the native basin defined by the
input structure
PART II Model-to-Model Comparisons of the GSM, ANM, and MD
THE MODELS A Brief Introduction
Models: ENM I • A single point (Cα) represents each residue
• Each point forms a node on a graph while edges represent the interactions, within a cutoff distance – Typically a single value is used for all interactions
• Anisotropic Network Model (ANM)
Models: ENM II • The key simplifying assumption made in
all ENMs is the harmonic approximation
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Models: ENM III
• Normal Modes characterize the correlated motions of the protein
• Longest timescales and largest amplitude motions are obtained from the lowest frequency modes
• A coarse-grained model that requires little computational time, even for large proteins
Models: MD I
• A comprehensive all-atom model – Classical, not QM
• Basic assumption of the model: – Protein behavior can be elucidated by
examining how it’s molecular structure evolves through a set of molecular steps under the influence of a specified potential or forcefield
Models: MD II
• A typical MD potential:
Models: MD III
• Thermal simulation: Proteins are hydrated The entire system of protein plus solvent is equilibrated at a specific temperature
• The benefit: Trajectory represents an ensemble in the thermodynamic sense
Methods • We selected 4 single domain proteins
(monomers)
• Assessment of similarity was done by comparing the top 20 mode spaces from each of the models, plus an experimental set
The 4 Target Proteins • 1A6N deoxy-myoglobin:
SCOP class α, 151 residues – The focus of these results
• 1WIT twitchin: SCOP class β, 93 residues
• 1UBQ ubiquitin:
SCOP class α+β, 76 residues • 1YPI triosephosphate isomerase:
SCOP class α/β, 247 residues
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
Results I: PC Projections
• PCs for the top 5 modes indicate degree of equilibration and mode space similarity – Fluctuations from FRODA and MD contrast a
thermal and mechanical simulation
PCs Using FRODA Modes
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
PCs Using MD Modes
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
PCs Using ANM Modes
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
ANM Consistency
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ANM_0_1 (.89) ANM_0_2 (92) ANM_0_3 (.90) ANM_0_4 (.90) ANM_0_5 (.95) ANM_0_6 (.93) ANM_0_7 (.89) ANM_0_8 (.92) ANM_0_9 (.89) ANM_0_10 (.92) ANM_0_11 (.91) ANM_0_12 (.92) ANM_0_13 (.92) ANM_0_14 (.91) ANM_0_15 (.89) ANM_0_16 (.90) ANM_0_17 (.92) ANM_0_18 (.94) ANM_0_19 (.89) ANM_0_20 (.89)
D
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
ANM essential subspaces are highly conserved when using multiple structures from a dynamic trajectory
FRODA Consistency
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FRODA-8 FRODA-20 ANM MD
A
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
FRODA is consistent across a range of parameter choices that control rigidity/flexibility
FRODA & MD Internal Consistency
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FRODA_I-II (.94) FRODA_I-ALL (.95)
FRODA_II-ALL (.97) MD_I-II (.81)
MD_I-ALL (.91) MD_II-ALL (.90)
C
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
FRODA and MD trajectories show internal consistency
Model Similarity
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MD_FRODA_8 (.57) MD_FRODA_20 (.58) FRODA-8_FRODA-20 (.93) A
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
All three models share much in common FRODA and ANM are much more alike than FRODA and MD or ANM and MD
Results IV • FRODA captures a set of 100
experimental structures as well as ANM, and significantly better than MD
Characterizing Protein Motions from Structure, Charles C. David, Donald J. Jacobs, Journal of Molecular Graphics and Modelling 31 (2011) 41–56
Please cite this article in press as: C.C. David, D.J. Jacobs, Characterizing protein motions from structure. J. Mol. Graph. Model. (2011),doi:10.1016/j.jmgm.2011.08.004
ARTICLE IN PRESSG ModelJMG 6108 1–16
14 C.C. David, D.J. Jacobs / Journal of Molecular Graphics and Modelling xxx (2011) xxx–xxx
examining the entire set of 20 PAs and the average COs. PA val-774
ues of less than 23◦ are considered to be within the small angle775
approximation and suggest excellent similarity. Fig. 8 shows the776
comparison of the model mode subspaces using the metric of777
PA, with RMSIP values shown parenthetically in the legend. From778
Fig. 8A, it is clear that the most similar mode subspaces are those779
from FRODA-8 and FRODA-20 with an RMSIP score of 0.93 and780
PAs less than 23◦ for the top fifteen modes. The next most simi-781
lar mode subspaces are from FRODA and ANM. These comparisons782
yield a RMSIP value near 0.75 and have PAs within the small783
angle approximation for six modes. The mode subspace compar-784
isons between ANM and MD and MD and FRODA are very similar,785
each having an RMSIP value between 0.5 and 0.6 and PA values786
less than 45◦ for the top five modes. While these angle values787
are not within the small angle approximation, they do indicate a788
good amount of similarity, commensurate with the good RMSIP789
score.790
The RMSIP scores between the model mode subspaces are791
shown for the four proteins investigated in Fig. 9 (left column).792
The average cumulative overlaps (for the entire set of 20 modes)793
between the model mode subspaces are shown in Fig. 9 (mid-794
dle column), and the first PA results are likewise shown in Fig. 9795
(right column). Again, it is clear that the ANM and FRODA mode796
subspaces are best able to capture each other’s essential motions.797
This was especially evident when looking at the top ten modes798
where the average CO remains greater than 0.70 (not shown).799
Additionally, ANM to MD as well as MD to FRODA maintain an800
average CO greater than 0.50 for the top 12 modes (not shown).801
While not excellent, these values parallel the results seen in Fig. 8802
and indicate a substantial amount of compatibility between the803
essential motions contained in these subspaces. Similar results804
were found for the other three SCOP classes of protein as shown805
in Fig. 9, with the RMSIP between FRODA and MD within the806
range of 0.51–0.63, and the RMSIP between ANM and FRODA807
within the range of 0.69–0.78 for all four SCOP classes. To put808
these values in perspective, the RMSIP between the FRODA-8809
and FRODA-20 modes spanned the range of 0.64–0.93 over the810
four studied proteins, indicating that the inter-model compar-811
isons were on par with the intra-model comparisons. For all four812
classes of proteins investigated, the ANM to MD RMSIP values813
were the lowest, spanning the range of (0.45–0.57). This result814
shows that ANM and MD are the most divergent of the three815
models investigated here. As Fig. 9 shows, there are no significant816
differences between the four proteins based on SCOP classifica-817
tion.818
3.7. Projection of experimental structures on the model modes819
An important consideration beyond the model-to-model com-820
parisons that have been performed is how well are actual821
experimental structures accommodated by the three different822
models. To address this question, a 20-dimensional subspace was823
derived from the experimental dataset of myoglobins, and com-824
pared to those obtained from each model. We are specifically825
assessing how well the 3 models under investigation were able826
to access the set of experimental structures given only the initial827
structure. Fig. 10A and B show the projection of the experimen-828
tal displacement vectors onto the model modes. In both panels,829
it is evident that the ANM mode space captures the experimen-830
tal displacements best, with FRODA doing almost as well in terms831
of both the size of conformational space defined by the top three832
modes and the significance of the overlaps generated therein. The833
MD based PCA mode space does significantly worse in terms of the834
amount of conformational space covered and fails to yield any sig-835
nificant overlap to the experimental displacements. These results836
are echoed in Fig. 10C showing the RMSIP values of ANM and FRODA837
Fig. 10. Experimental and model subspace comparisons. Projection of the experi-mental displacement vectors on model modes 1, 2 (Top A) and on modes 2, 3 (middleB). The PA results from comparing the experimentally derived mode space to themodel mode spaces, with the RMSIP values shown parenthetically in the legend(bottom C). The level line is drawn for PA value 23◦ in C.
mode subspaces to the experimental mode subspace are about 0.60 838
while the RMSIP value of the MD mode subspace to the experi- 839
mental mode subspace is only 0.44, a significantly lower result. 840
Taken together, these results indicate that both ANM and FRODA 841
are able to capture the majority of the displacements seen in the 842
experimental structures, while MD captures significantly less of the 843
displacements. 844
Conclusions • The simulated structures project differentially
into the model mode spaces, but reveal significant overlap in the Essential Subspaces
• The models show solid intra-consistency
• There is substantial inter-consistency – MD is unique in its ability to sample outside the
native basin defined by the input structure • MD thus yields distinctive results
• The FRODA and ANM Essential Subspaces capture the experimental set of structures best
PART III Application of the GSM to myosin V
Introduction I • Myosins are molecular motors capable of
converting chemical energy into mechanical work through a cyclic interaction with actin filaments. Myosin V (MV) below:
Myosin V Dynamics
Introduction II • We collaborated with experimentalists who study
myosins using FRET
• FRET allows us to determine the distance between a donor and acceptor probe
PROJECT I Applying the GSM to myosin V
Introduction
• We selected a subset of 106 residues that defined the nucleotide-binding pocket (NBP)
• We investigated how conformational changes in the NBP are communicated to the lever arm and actin-binding cleft (ABC)
Myosin V showing NBP
Methods • We explore ED of MV using the GSM starting
with three different X-ray crystal structures (1OE9, 1W7J, 1W7I)
• Our results are based on dPCA, compatible with our focus on three residues (171, 294, 525)
Myosin V Showing NBP, ATP, and residues 171, 294, 525
Results • We obtained distinct distributions for the 171-294 distance in
the MV.ATP structure and the MV.ADP structure – Thus, the MV.ADP structure is not capable of converting to the closed
pocket conformation without significant constraint breaking
• For the MV.ADP state, very few modes of pocket opening/closing agree with experiment – The crystal structure represents the weak, open pocket MV.ADP state
• We saw more evidence for a novel post-power-stroke MV.ADP state – NBP and ABC are both closed – This is the strong closed pocket MV.ADP state – This state has not yet been crystalized
Jacobs, D.J., et al., Kinetics and thermodynamics of the rate-limiting conformational change in the actomyosin V mechanochemical cycle. J Mol Biol. 407(5): p. 716-30. Sun, M., et al., Characterization of the pre-force-generation state in the actomyosin cross-bridge cycle. Proc Natl Acad Sci U S A, 2008. 105(25): p. 8631-6.
Results of dPCA analysis based on the relative motions of three residue pairs: 294-171, 171-525, and 294-525, in all three crystal structures. (ADP.BeFX is an ATP mimic)
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Kinetics and Thermodynamics of the Rate Limiting Conformational Change in the myosin V Mechanochemical Cycle. (2011). Donald J. Jacobs, Darshan Trivedi, Charles C. David, and Christopher M. Yengo, Journal of Molecular Biology, Apr 15;407(5):716-30
Mode 1 from dPCA MV.ATP
Results of dPCA analysis based on the relative motions of three residue pairs: 294-171, 171-525, and 294-525, in all three crystal structures. (ADP.BeFX is an ATP mimic)
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Kinetics and Thermodynamics of the Rate Limiting Conformational Change in the myosin V Mechanochemical Cycle. (2011). Donald J. Jacobs, Darshan Trivedi, Charles C. David, and Christopher M. Yengo, Journal of Molecular Biology, Apr 15;407(5):716-30
Mode 1 from dPCA MV.ATP
PROJECT II Applying the GSM to myosin V
Introduction I
• Understanding the mechanism of force generation in MV requires elucidating allosteric communication pathways critical to motor function
• Three well conserved regions involved: – The P-loop – Switch I – Switch II
Switch II Mutants Reveal Coupling Between the Nucleotide- and Actin-Binding Regions in Myosin V Darshan V. Trivedi, Charles C. David, Donald J. Jacobs, and Christopher M. Yengo, Biophysical Journal Volume 102 Issue 11 pp.2545-2555. doi:10.1016/j.bpj.2012.04.025
Introduction II • Switch I is chiefly involved in the communication
pathways between the active site and the ABC
• Switch II mediates the communication to the converter-lever arm domain
• To understand how Switch II affects the conformational dynamics of the NBP and ABC, we introduced two single site mutations
– G440A: Eliminates a highly conserved hydrogen bond to the gamma phosphate of ATP
– E442A: Eliminates a highly conserved salt bridge between Switch I and Switch II
Methods
• We defined three subsets: – NBP [106] – Actin Binding Region (ABR) [455] – A proposed Communication Pathway (CP) [89]
• Conformational changes in these subsets were investigated using GSM with ED
Myosin V showing ABR
Results I • Switch I-Switch II interactions stabilize the closed nucleotide
binding pocket conformation in the absence of actin
• The NBP in the ATP state had reduced dynamics of Switch I in the G440A mutant – This hinders Switch I-Switch II interactions – Reduces the stability of the closed NBP conformation
• The mobility of the P loop is increased by both Switch II mutants
Switch II Mutants Reveal Coupling Between the Nucleotide- and Actin-Binding Regions in Myosin V Darshan V. Trivedi, Charles C. David, Donald J. Jacobs, and Christopher M. Yengo, Biophysical Journal Volume 102 Issue 11 pp.2545-2555. doi:10.1016/j.bpj.2012.04.025
The first PC mode of the NBP of mutant and wild-type myosin V
Results II • The G440A mutation alters ABR dynamics
– In the rigor state, the G440A mutant increases dynamics of a region of the U50 domain: • The cardiomyopathy loop • The C-terminus of the HO-helix
– There is a dramatic increase in the mobility of helix-loop-helix region of the L50 domain
• The G440A mutation makes F441 highly dynamic in the ATP state – Disruption of Switch II rotation by G440A alters the mobility of F441 – This hinders F441 interaction with the surrounding hydrophobic
environment
• These two alterations result in disruption of the communication pathways between the active site and the U50 and L50 regions
The first PC mode of the ABR of mutant and wild-type myosin V
Switch II Mutants Reveal Coupling Between the Nucleotide- and Actin-Binding Regions in Myosin V Darshan V. Trivedi, Charles C. David, Donald J. Jacobs, and Christopher M. Yengo, Biophysical Journal Volume 102 Issue 11 pp.2545-2555. doi:10.1016/j.bpj.2012.04.025
CONCLUSION Summary of the Work
Summary • We have established the GSM as a viable alternative and/or
co-model to either an ENM or MD
• The GSM is both efficient and effective at determining the native state dynamics of a protein – The GSM is qualitatively and quantitatively similar to MD and ANM
• The GSM is scalable – Applied to a wide range of proteins with success including small, single
domain proteins and large multi-domain, multi-state proteins like MV
• ED of GSM trajectories is an effective method to tease out the biological motions of a subset of residues in a protein
Thank You! • Mentors, Colleagues, Friends, & Family • UNCC for my financial aid • NIH for supporting my research