Using Molecular Simulation to
Model High-Resolution Cryo-EM
, Justus Loerke
, Elmar Behrmann
Christian M.T. Spahn
, Karissa Y. Sanbonmatsu
*Department of Chemistry, New York University, Abu Dhabi, United Arab Emirates
New Mexico Consortium, Los Alamos, New Mexico, USA
Theoretical Biology and Biophysics, Theoretical Division, Los Alamos National Laboratory, Los Alamos,
New Mexico, USA
Institut f€ur Medizinische Physik und Biophysik, Charite
¨tsmedizin Berlin, Berlin, Germany
Structural Dynamics of Proteins, Center of Advanced European Studies and Research (CAESAR), Bonn,
Corresponding author: e-mail address: firstname.lastname@example.org
1. Introduction 498
2. Theory 501
2.1 Molecular Model 501
2.2 Scoring Function 502
2.3 Masking the Cryo-EM Map 502
3. Methods 503
4. Results 505
5. Summary 508
An explosion of new data from high-resolution cryo-electron microscopy (cryo-EM)
studies has produced a large number of data sets for many species of ribosomes in
various functional states over the past few years. While many methods exist to produce
structural models for lower resolution cryo-EM reconstructions, high-resolution recon-
structions are often modeled using crystallographic techniques and extensive manual
intervention. Here, we present an automated fitting technique for high-resolution cryo-
EM data sets that produces all-atom models highly consistent with the EM density.
Using a molecular dynamics approach, atomic positions are optimized with a potential
that includes the cross-correlation coefficient between the structural model and
the cryo-EM electron density, as well as a biasing potential preserving the stereochem-
istry and secondary structure of the biomolecule. Specifically, we use a hybrid
Methods in Enzymology #2015 Elsevier Inc.
ISSN 0076-6879 All rights reserved.
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structure-based/ab initio molecular dynamics potential to extend molecular dynamics
fitting. In addition, we find that simulated annealing integration, as opposed to straight-
forward molecular dynamics integration, significantly improves performance. We obtain
atomistic models of the human ribosome consistent with high-resolution cryo-EM
reconstructions of the human ribosome. Automated methods such as these have
the potential to produce atomistic models for a large number of ribosome complexes
simultaneously that can be subsequently refined manually.
Mechanistic studies of the bacterial ribosome over the past decade
have proceeded at a rapid rate, elucidating many of the steps of protein syn-
thesis elongation. In addition to crystallographic (Dunkle et al., 2011;
Tourigny, Fernandez, Kelley, & Ramakrishnan, 2013), cryo-electron
microscopy (cryo-EM) (Dashti et al., 2014), single molecule (Blanchard,
Kim, Gonzalez, Puglisi, & Chu, 2004; Munro, Wasserman, Altman,
Wang, & Blanchard, 2010; Olivier et al., 2014; Wang et al., 2012) and rapid
kinetics studies (Rodnina & Wintermeyer, 2011), computational studies by
other groups have been performed on ratchet motion (Bock et al., 2013;
Ishida & Matsumoto, 2014; Kurkcuoglu, Doruker, Sen, Kloczkowski, &
Jernigan, 2008; Trylska, Konecny, Tama, Brooks, & McCammon, 2004),
decoding (Adamczyk & Warshel, 2011; Zeng, Chugh, Casiano-Negroni,
Al-Hashimi, & Brooks, 2014), protein translocation (Ishida & Hayward,
2008; Rychkova, Mukherjee, Bora, & Warshel, 2013), and other aspects
of the ribosome (Baker, Sept, Joseph, Holst, & McCammon, 2001;
Trabuco et al., 2010). Outstanding research has advanced molecular dynam-
ics of RNA (Bergonzo et al., 2014; Cheatham & Case, 2013; Chen,
Marucho, Baker, & Pappu, 2009; Henriksen, Davis, & Cheatham, 2012;
Liu, Janowski, & Case, 2015). The publication of the first crystal structure
of a eukaryotic ribosome in 2011 has opened the field to new possibilities, as
variable regions of the eukaryotic ribosome are thought to be conduits to a
large number of posttranscriptional regulatory pathways (Ben-Shem et al.,
2011; Jenner et al., 2012; Melnikov et al., 2012). Cryo-EM has played a
key role in elucidating the structure and function of ribosome complexes:
large-scale conformational changes, movement of ligands through the
ribosome, factor-binding interactions, along with many other aspects of
ribosome function have been advanced by cryo-EM (Agrawal et al.,
1996, 2000; Beckmann et al., 2001; Connell et al., 2008; Frank &
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Agrawal, 2000; Frank, Radermacher, Wagenknecht, & Verschoor, 1988;
Frank et al., 1995; Ratje et al., 2010; Schuette et al., 2009; Spahn et al.,
2001, 2004; Valle et al., 2002, 2003; Villa et al., 2009; Wagenknecht,
Carazo, Radermacher, & Frank, 1989). The recent advent of direct electron
detectors has opened a new frontier for cryo-EM, producing 3D structures
of the ribosome with comparable resolution to X-ray crystallography
(Amunts et al., 2014; Fernandez, Bai, Murshudov, Scheres, &
Ramakrishnan, 2014; Fernandez et al., 2013).
Over the past decade, a variety of techniques have been developed to
produce 3D models of the ribosome consistent with cryo-EM reconstruc-
tions, including real-space refinement (Gao et al., 2003), normal mode
fitting (Gorba, Miyashita, & Tama, 2008), and molecular dynamics simula-
tion (Budkevich et al., 2014; Muhs et al., 2015; Orzechowski & Tama,
2008; Ratje et al., 2010; Trabuco, Villa, Mitra, Frank, & Schulten, 2008;
Villa et al., 2009; Whitford et al., 2011), among others. Real-space refine-
ment showed details of intersubunit rotation (Gao et al., 2003), while nor-
mal mode flexible fitting produced models of EF-G complexed with the
ribosome in various functional states (Gorba et al., 2008). A landmark study
used molecular dynamics simulation biased by cryo-EM electron density
(MDFF) to produce more accurate models of the ternary complex bound
to the ribosome (Trabuco et al., 2008; Villa et al., 2009). A similar method
was developed simultaneously by Tama and coworkers (Orzechowski &
Tama, 2008). The above method also produced new insights into the
protein-conducting channel by a bound ribosome, and translational stalling
in bacterial and eukaryotic systems (Armache et al., 2010; Becker et al.,
2011; Seidelt et al., 2009). Structure-based molecular dynamics fitting
(MDfit) methods allow molecular fitting that preserves stereochemistry pre-
sent in initial starting structures, while offering the key advantage of running
on a single desktop workstation (Muhs et al., 2015; Ratje et al., 2010;
Whitford et al., 2011). This method revealed new translocational interme-
diates and a novel conformational change of the mammalian ribosome
(Budkevich et al., 2014; Ratje et al., 2010).
More specifically, the MDfit method begins with a potential energy
function based on the initial configuration. An energetic weight based on
knowledge of the target is introduced, yielding a downhill energy profile,
where the target configuration corresponds to the global minimum. For
example, to obtain structural models of the bacterial ribosome in the rotated
configuration, we defined a starting potential energy function based on a
classical ribosome configuration. We defined a biasing term based on
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correlations between the cryo-EM reconstruction of the rotated state and
the simulated density, determined from snapshots of the simulated structure
throughout the simulation. This produced all-atom models highly consistent
with cryo-EM reconstructions of the rotated states and also revealed the
configurations (Ratje et al., 2010). The method was also
used to construct one of the first all-atom models of the human ribosome,
revealing a new conformational change specific to eukaryotic ribosomes
(subunit rolling) (Budkevich et al., 2014).
The advent of direct-detector high-resolution cryo-EM studies and
high-resolution eukaryotic ribosome structures is fueling a renaissance in
ribosome mechanism (Amunts et al., 2014; Ben-Shem et al., 2011;
Fernandez et al., 2013, 2014; Jenner et al., 2012). Higher resolution
cryo-EM now allows many species of ribosomes to be captured in a wide
range of functional states. With regard to eukaryotic ribosome research
(80S ribosome), external regions of the ribosome have highly variable
sequences and are thought to bind a variety of factors involved in posttran-
scriptional gene regulation ( Jenner et al., 2012). In addition, comparison
between human and bacterial ribosomes is essential to understand antibiotic
action, as the ribosome is one of the main antibiotic targets. In light of the
numerous new high-resolution cryo-EM structures of the ribosome
(Amunts et al., 2014; Fernandez et al., 2013, 2014), there is high demand
for methods capable of producing all-atom models consistent with these
data. The methods described above are predominantly based on lower res-
olution data and leverage the lower resolution, either by using coarse-
grained approaches, constraints, or native state biases (Ahmed, Whitford,
Sanbonmatsu, & Tama, 2012; Ratje et al., 2010; Trabuco et al., 2008;
Wang & Schroder, 2012). We note that one new successful and promising
method uses self-guided Langevin dynamics (Wu, Subramaniam, Case,
Wu, & Brooks, 2013). There are few fully automated methods tailored to
produce all-atom models highly consistent with the new high-resolution
cryo-EM data. Currently, some groups are using existing crystallography
software (Amunts et al., 2014; Fernandez et al., 2013, 2014) and adjustments
of domains and subregions of the macromolecular complex for the fitting
process. Automating portions of this process has the potential to increase
efficiency and accuracy. Here, we extend the MDfit method by combining
an ab initio molecular dynamics potential with the all-atom structure-based
potential, maintaining the capability to preserve the stereochemistry of
initial models while simultaneously accessing alternative folds. Following
the Korostelev et al. crystallographic refinement by simulating annealing
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and other treatments (Brunger, Kuriyan, & Karplus, 1987; Korostelev,
Laurberg, & Noller, 2009), we employ a simulating annealing strategy, as
opposed to a straightforward molecular dynamics sampling.
The aim is to fit the atomic structure to high-resolution density
derived from the cryo-EM reconstruction while maintaining correct stereo-
chemistry. We merge two previous molecular simulation techniques in an
effort to improve the fit: (i) an ab initio force field (Trabuco et al., 2008) and
(ii) a structure-based potential that preserves the native stereochemistry and
3D fold of the initial structure (Ratje et al., 2010; Whitford et al., 2011).
Specifically, we use a scoring function:
E¼ERðÞ+ENC RðÞ+w1CCCðÞ (1)
here, Ris the molecular coordinate vector, E(R) is the molecular potential
energy term, and E
(R) is the native contact potential bias that restrains the
atomic model to preserve its secondary structure and maintains tertiary
native contacts. While this term is a localized potential, it effectively biases
the system toward the overall 3D fold of the initial starting structure. The last
term is the biasing function that creates a downhill potential, moving the
atomic coordinates toward the cryo-EM map. Details of each term and their
weighting are described below.
2.1 Molecular Model
The first term in Eq. (1) is the potential energy of the molecular model. This
term includes the energy contribution from all bonding terms of the classical
molecular mechanics force field, including bond, angle, torsion, and
improper torsion, as well as a nonbonding term to account for volume
exclusion. The nonbonding term is a pairwise summation of all-atom pairs,
ij , where C12
is a constant derived from van der Waals
parameters of each atom pair i,jwith ij>4. To maintain the native con-
tacts and stereochemistry, an additional potential term was introduced. For a
given reference structure coordinate set, R
(for example, an atomic model
that comes from crystallography experiments), we compute all pairwise con-
tacts for pairs such that ij>4 and with a distance cutoff condition of
. These contacts are protected by adding a term to
the molecular potential. For a given configuration represented by coordinate
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R, this term is a summation of all pairwise contacts
here, λis the strength of native contact potential bias. We use
10 <λ<50 kJ/nm
in our study.
2.2 Scoring Function
To measure the quality of fit and bias the atomic model toward the cryo-EM
map, we used a cross-correlation function, which is introduced in earlier
publications (Gorba et al., 2008; Ratje et al., 2010). Cryo-EM reconstruc-
tions are represented by intensities on a cubic lattice stored in a vector
(k), where kis the index for grid space points in all directions. To mea-
sure the quality of fit between the map and the atomic model, a simulated
map is computed from atomic coordinates using the same grid spacing as
the experimental map and assuming a Gaussian distribution of electron
density for each atom. The simulated electron density at grid site kdue to
atom jat r
where 2σis the resolution of cryo-EM map.
The similarity between the cryo-EM map and the simulated map is com-
puted in a similar manner to MDfit with a cross-correlation function of the
2.3 Masking the Cryo-EM Map
In certain cases, a small region of cryo-EM electron density may correspond
to an unresolved binding factor or a highly dynamic region of the ribosome
that resides in multiple states that are difficult to separate during clustering.
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Since a given atomic model represents only one conformational state in a fit,
these regions cannot be fit by a single atomistic model. Elimination of these
regions produces a cleaner map with less space to search for a better fit. To
eliminate the extra occupancy in the electron density, we define a vector,
), where Nis the total number of grid points in the simulated
and experimental cryo-EM maps. Each element of the vector is filled as:
Our filtered map is given by ρ0EM ¼ρEM qwhere symbol denotes the
element wise product.
To effectively search the conformational space, we used the modified
potential described above with a simulated annealing strategy. The con-
straints to the native topology are added by using the genres module of
GROMACS. The attractive part of the Lennard–Jones interaction was set
to zero in the program. The method used the MDfit code as a starting point,
which itself is a modified version of gromacs 4.5.5. The calculations are per-
formed with a desktop computer. No specialized hardware is required.
We integrate the equations of motion using stochastic dynamics where a
friction term and a noise term are added to Newton’s equation of motion as
is the friction coefficient for particle iand R
is the noise term
satisfying the fluctuation-dissipation theorem as RitðÞRjt+sðÞ
For the ab initio portion of the potential, we use GROMOS force field
with 53A6 parameter set (Oostenbrink, Villa, Mark, & Van Gunsteren,
2004). We emphasize that the method is not limited to a particular force field
and that any ab initio molecular dynamics force field can be applied.
To effectively find the optimum fit, we implement simulated annealing.
Here, the temperature of the simulation is reduced in nstages. At the begin-
ning of each stage, we set the temperature to Tn¼T0=2n1ðÞ
, where T
the initial temperature. Each simulated annealing simulation started with
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an initial temperature of T0¼500 K. We cool the system from 500 K to
a final temperature of 15 K and we repeat the procedure for three times
in each fit.
Our protocol of fitting the high-resolution cryo-EM map is illustrated in
Fig. 1. The method starts with rigid body fitting of the model to the cryo-
EM map using Chimera (Goddard, Huang, & Ferrin, 2005). Next, we use
simulated annealing molecular dynamics to sample the conformational space
of the modified potential given in Eq. (1), slowly cooling the model from
500 to 15 K, repeating three times.
Figure 1 A schematic description of the multistep fitting of atomic models to
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The rigid body fit may not produce a high correlation between the
atomic model and the cryo-EM map. If there is a significant difference
between the model and map, then a high bias toward the map may distort
the structure. Therefore, the biasing strength toward the cryo-EM map is
low in our first iteration. The bias to the native contacts is high at this stage.
To achieve this, we use a smaller value of w¼Natoms (see Eq. 1), where
is the number of atoms in the molecule. After the simulation is com-
pleted, we choose the structure with the highest cross-correlation coefficient
(CCC) as the current model and move to the masking stage of our protocol.
To mask the map, we created a vector of zeros and ones from the best-fitted
model (see Eq. 5). This vector is multiplied pairwise with the original cryo-
EM map as detailed above. The grid points that are zero in the simulated map
become zero in the original map. The masked map is used to launch another
simulated annealing molecular dynamics simulation. Here, we use a higher
weight to bias our model toward the cryo-EM map. For that reason, we
choose w¼mNatoms where mstarts at 2 and is incrementally increased in
Importantly, our fits include two different biasing terms with adjustable
weights. One corresponds to the bias toward native contacts, while the sec-
ond bias is toward the cryo-EM reconstruct. To prevent overfitting, we
chose these such that the two are on the same order of magnitude.
To test the protocol, we study two model systems. Model I is the h40–
h44 region of the small subunit of the human ribosome. Figure 2 shows its
structure before and after fitting to the cryo-EM reconstruction at near-
atomic resolution. Model II is the entire small subunit of the protein–
RNA complex of the human ribosome (Fig. 3). The initial atomic model
for each structure used our previous all-atom model of the human ribosome
as a starting point (Budkevich et al., 2014).
To effectively search the conformational space of the modified potential,
we used stochastic dynamics. In obtaining the optimum value for the friction
term in Eq. (6), we note that lower friction coefficients often improve sam-
pling. However, this value also needs to be sufficiently high to remove the
excess heat produced during minimization. Figure 4 shows the time evolu-
tion of cross-correlation coefficient (Eq. 4) for different friction coefficients.
At the lowest value of friction coefficient γ¼0:01 1=ps
, the conforma-
tional search fails to sample the modified potential effectively. Higher
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friction coefficients such as 1 γ100 1=psðÞ, however, display an increase
in the CCC.
We emphasize that our method uses a hybrid potential, generalizing the
structure-based potential to also include ab initio molecular dynamics poten-
tial terms. To understand additional effects, such as (a) changing the integra-
tion to a simulated annealing protocol and (b) filtering the map to remove
unresolved regions, we performed a comparison study with three cases:
(i) straightforward molecular dynamics integration, (ii) simulated annealing,
and (iii) simulated annealing plus filtering. In this comparison, we are inter-
ested in finding the method that gives the highest score in the correlation
coefficient when sufficient sampling is performed (Fig. 5). Using an equal
time of simulation in each protocol, we find that simulated annealing
Before ﬁt After ﬁt
Figure 2 Atomic model of a small region from human ribosome before flexible fitting
by the simulated annealing molecular dynamics (A), and after the fit (B–D).
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molecular dynamics gives a higher correlation score than straightforward
molecular dynamics integration. Interestingly, our protocol of filtering
the map further improves the overall fit. A critical consideration is that
for a given conformation, the correlation coefficient computed from itera-
tion nwill always be higher than when the map of the previous iteration
n1 is used. This follows from the fact that filtering reduces the number
of nonzero grid points, thus reducing the denominator of the CCC in
Eq. (4). This is not desirable since a configuration must have the same value
of CCC between each iteration so that we can compare the progress over
time. To account for this, we normalize the CCC of a given configuration,
Rin iteration nas CCCnRðÞ¼CCCn1R0
Figure 3 Same as Figure 2 this time for the entire small subunit.
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ðÞis the correlation coefficient of a reference configura-
at iteration n1, CCC
) is its value in iteration n(due to the
change in the map), and CCC
(R) is the correlation of Rin iteration n
before the normalization. Using this method, we compute the CCC
between each iteration. Our results show an improvement in CCC scores
for Model II. We obtain a similar performance in Model I. Our results show
0.812, 0.821, and 0.827 for the maximum CCC score for MD, simulated
annealing, and simulated annealing with filtering, respectively. Figure 6
shows the fitted structure together with the change in correlation coefficient
during the simulations.
We have adapted the MDfit technique to high-resolution cryo-EM
data by including an ab initio molecular dynamics potential, allowing
0 200 400 600 800 1000
Correlation coefﬁcient (CC)
g = 0.01
g = 1
g = 100
g = 10
Figure 4 Time evolution of correlation coefficient as a function of the friction coeffi-
cient, γused in stochastic molecular dynamics simulation method.
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Figure 6 Example of fitting atomic model to high-resolution cryo-EM reconstruction of
the human ribosome. (A) Cryo-EM map of h40–h44 segment. Fitted atomic model is rep-
resented by stick representation, while green mesh is the high-resolution cryo-EM map.
The resulted fit is achieved by optimizing the correlation between the atomic model
and cryo-EM map while preserving the stereochemistry. This is achieved by
simulated annealing molecular dynamic simulations. (B) Time evolution of fit during
0 200 400 600 800 1000 1200
Correlation coefﬁcient (CC)
Time (× 1000 steps)
Figure 5 Comparison of three searching methods toward converging to their highest
correlation coefficient value. Gray stars, molecular dynamics simulation at 300 K; solid
lines, simulated annealing molecular dynamics; circles, simulated annealing with
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alternative folds from the native configuration. Employing a simulated
annealing strategy, we improved performance, allowing us to automatically
produce all-atom models highly consistent with high-resolution cryo-EM
reconstructions, given an initial model of the complex. Such automated
methods have the potential to enable rapid fitting of many ribosome com-
plexes simultaneously, which can then be refined with manual
The technique runs on a desktop computer with relatively modest com-
pute requirements and can accommodate conformational changes of large
molecular assemblies. A key advantage is the speed of sampling. We note
that MDfit was previously used to fit a classical P/P tRNA configuration
to a hybrid P/E-like configuration, requiring a tRNA movement of
˚. Thus, one could either use the current method to attempt large con-
formational changes, or apply the standard MDfit to achieve large confor-
mational changes and refine with the current technique, which allows
ab initio fitting of local geometry based on classical mechanics force fields
with multiple torsional minima, and thus enables a search of all rotamers.
The fits show significant improvement on molprobity scores for the final
fitted structures, reflecting improved agreement with local stereochemistry.
We note that nonuniformity in map resolution and long-range electrostatic
interactions are also important issues (Hayes et al., 2014).
This work was supported by the National Science Foundation, the Human Frontiers Science
Program, and the National Institutes of Health.
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