Amortized Inference for Heterogeneous Reconstruction in Cryo-EM
Anonymous Author(s)
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Abstract
Cryo-electron microscopy (cryo-EM) is an imaging modality that provides uniqueinsights into the dynamics of proteins and other building blocks of life.
The algorithmic challenge of jointly estimating the poses, 3D structure, and conformationalheterogeneity of a biomolecule from millions of noisy and randomly oriented 2Dprojections in a computationally efficient manner, however, remains unsolved.
Ourmethod, cryoFIRE, performs ab initio heterogeneous reconstruction with unknownposes in an amortized framework, thereby avoiding the computationally expensivestep of pose search while enabling the analysis of conformational heterogeneity.
Poses and conformation are jointly estimated by an encoder while a physics-baseddecoder aggregates the images into an implicit neural representation of the conformational space.
We show that our method can provide one order of magnitudespeedup on datasets containing millions of images, without any loss of accuracy.
We validate that the joint estimation of poses and conformations can be amortizedover the size of the dataset.
For the first time, we prove that an amortized methodcan extract interpretable dynamic information from experimental datasets.
Introduction
Proteins and other biological macromolecules in the cell function through a finely-tuned choreographyof transitions between metastable conformational states.
Analyzing the structural heterogeneity ofa biomolecule is therefore critical for applications such as drug design and, more generally, forunderstanding these essential building blocks of life.
In a single particle cryo-electron microscopy(cryo-EM) experiment, a set of biomolecules whose structures sample some thermodynamic distribution are flash-frozen in a thin layer of vitreous ice and imaged with a transmission electron microscope(Fig.
1 (a)).
A cryo-EM experiment outputs a large set of unlabeled images, each containing a uniqueprojected molecule that adopts an unknown conformation and is viewed from an unknown orientation( pose ) ϕ
i =
( R i , t i ) ∈
SO (3) × R 2 (Fig. 1 (b)).
While homogeneous reconstruction methods focuson estimating the average 3D structure (the consensus volume) of the studied molecule from thecollected images, heterogeneous methods take into account structural variability and introduce avariable
z i (the conformational state ) that characterizes the electron scattering potential (the volume )
V ( ., z i ) : R 3 → R associated with observation i [6].
Given the image formation model (detailed in
Section 3.1), heterogeneous reconstruction can be seen as an inverse problem where V , z i and ϕ imust be inferred from the images Y i .
A graphical formulation of the problem is given in Fig.
1 (c).
Spurred by recent advances in data collection capabilities, the number of images collected per cryoEM experiments has been steadily increasing, now reaching millions to tens of millions [2, 20].
Established methods break down 3D reconstruction into two alternating iterative refinement steps:1) the latent pose ϕ
i and conformational states z i are first estimated from the images and the currentestimate of V , and 2) the estimation of V is then updated using the current estimates of the latent
[Figure]
variables.
The primary computational bottleneck of this approach is pose estimation, which is doneby rendering images from view points distributed on the the 5-dimensional space SO (3) × R 2 .
Although previous methods came up with accelerated branch-and-bound [15] strategies, state-of-theart methods for pose search raise two problems: (1) solving this problem for a single image is timeconsuming, especially when the images are rendered using a neural model [40] and (2) the pose needsto be solved independently for each image in the dataset and does not use the fact that similar imagesare likely associated with the similar variables.
Furthermore, most heterogeneous reconstructionalgorithms limit their applicability by relying on an upstream homogeneous reconstruction, treatingposes as known to simplify the optimization problem for z
i or due to the sheer computational cost ofpose search.
In this work, we present a heterogeneous cryo-EM reconstruction method that amortizes (over thesize of the dataset) the cost of inference for latent variables, by learning a function that directly mapsimages to posterior distributions.
Our method addresses both the increasing size of datasets and theopportunity to learn complex conformational spaces of dynamic proteins, while performing ab initioreconstruction, meaning it does not need an upstream homogeneous reconstruction.
Previous methodsshowed that the estimation of z i could be amortized in heterogeneous reconstruction [38, 40, 5, 41]and that the estimation of ϕ i could be amortized in homogeneous reconstruction [21, 17] but no jointlyamortized inference technique was proven to work on experimental datasets.
By leveraging a tailoredloss function and using a specialized autoencoder-like architecture, cryoFIRE (Fast heterogeneous ab Initio Reconstruction for cryo-EM) jointly amortizes the estimation of poses and conformations overthe size of the dataset.
Our contributions include:
• an autoencoder-based architecture that process images 10 times faster than existing methods
and enables amortization of the runtime over the size of the dataset,
• a demonstration that our model accurately learns the structure of a low-dimensional mani-
fold in the conformational space on benchmark synthetic datasets with both discrete and
continuous heterogeneity, and
• the first instance of amortized inference for ab initio heterogeneous reconstruction of
experimental cryo-EM datasets.
Related Work
Heterogeneous reconstruction methods must jointly infer the conformational space V and the latentvariables (the poses ϕ
and the conformational states z i ).
All existing methods make this problemtractable using an iterative strategy that alternates between the estimation of V and the estimation ofthe latent variables.
They can all be differentiated depending on how latent variables are estimated [6].
Expectation-Maximization over Conformations With an Expectation-Maximization (EM) algorithm, posterior distributions over the conformational states are computed (or approximated) for eachimage at expectation step.
In cryo-EM, this method was first popularized by RELION with 3D Classification [30] which implemented a discrete class indicator z i ∈ { 1 , . . .
, K } , where K is the numberof classes defined by the user.
More recently, a continuous reconstruction method called multi-bodyrefinement was made available in RELION [19].
In this approach, a homogeneous reconstruction issegmented by the user into a set of rigid bodies, where each rigid body is free to move relative to theothers.
The relative pose (orientation and translation) of each body is subsequently estimated through EM for each particle, and further reduced through Principal Component Analysis (PCA).
Variousmethods have been developed to estimate the conformational space as a linear deformation arounda known reference.
HEMNMA [10] uses the normal modes, or eigenvolumes, of the reference tomodel its deformation and proceeds through a projection-matching-based elastic alignment of eachsingle-particle image with the reference structure to yield a reduced representation of the variabilityin the dataset. 3DVA [24] relaxes the dependence on known normal modes and instead implements avariant of the EM algorithm for Probabilistic PCA which iteratively updates the eigenvolumes andthe projection of the particles on them, until convergence, following [33].
Other approaches explicitlyestimate the deformation field mapping the reference structure to the best-fit structure for each image.
In Herreros et al.
[9], the deformation field is defined as a linear expansion over Zernike polynomials,with z i as their coefficients.
In 3DFlex [23], the deformation field is generated from z i through aneural flow generator, alleviating the linear constraint.
Formally, each z i can be seen as a pointestimate that maximizes the posterior distribution over conformational states.
An in-depth review of EM-based reconstruction method can be found in [32].
Other computational approaches like Markov
Chain Monte Carlo have been explored for ab initio heterogeneous reconstruction in [16], introducinga mathematical framework for representing deformable molecules (“hyper-molecules”), but remain aprototype implementation.
Amortization over Conformations Instead of optimizing each variable independently, amortizedinference learns a function q ψ , parameterized by ψ , that maps images Y i to probability (posterior)distributions over the space of latent variables [12].
If N represents the size of the dataset, amortizedinference therefore replaces the estimation of N latent variables with the learning of ψ , whichcomplexity (number of dimensions) does not scale with N .
Previous methods explored the possibilityof using amortized inference to estimate the conformational state
z i , in a setting where the poseswere known. CryoDRGN [38] introduced amortized variational inference to estimate the conformational state z i in the setting where poses are known.
In cryoDRGN [38], distributions over theconformational states are predicted by the encoder of a Variational Autoencoder (VAE) [12, 13]and the conformational space is parameterized with an implicit neural representation.
E2GMM [5]and cryoFold [41] both reconstruct a deformable atomic representation of the molecule and train anencoder to associate each image with a low-dimensional z i that characterizes the deformation.
Thesetwo methods require the initialization of the backbone structure of the molecule.
Although thesemethods can be used to analyze the structural heterogeneity in a dataset, they assume the poses to begiven by another reconstruction method.
In cryoDRGN-BNB [39] and cryoDRGN2 [40] the posesare not given anymore but instead are estimated using an exhaustive search strategy.
The estimation ofthe poses therefore does not amortize over the size of the dataset and, in spite of a branch-and-boundapproach [15], the 5D pose search remains the most computationally expensive step in the pipeline.
Amortization over Poses In the context of homogeneous reconstruction, previous methods usedamortized inference to predict the latent variables.
In cryoVAEGAN [18], Miolane et al.
showed thatthe in-plane rotation and the contrast transfer function (CTF) parameters could be jointly estimatedin the latent space of an encoder.
CryoGAN [7] showed that homogeneous reconstruction couldbe achieved with a generative framework using a discriminative loss to avoid explicitly recoveringthe poses, considered as “nuisance” variables.
SpatialVAE [3] showed that the translations and thein-plane rotations in 2D images could be estimated with a VAE-based architecture, and was latergeneralized to other transformations in [35].
CryoPoseNet [21] first demonstrated the possibility ofusing an autoencoder architecture with synthetic datasets.
CryoAI [17] later introduced the symmetricloss to help the model avoid local minima and showed that homogeneous reconstruction could bedone on experimental datasets.
All of these methods, however, reconstruct a 3D consensus volumeand do not address the question of conformational heterogeneity.
Joint Amortization Rosenbaum et al .
[27] were the first to demonstrate heterogeneous reconstructionfrom unknown poses in a jointly amortized framework on synthetic data: both z i and ϕ are estimated with a variational encoder and predicted conformations are used to deform an atomic model, whilepredicted poses are used to compute projections analytically.
The method was only proven to workon simulated datasets and the atomic representation needs to be initialized from a known backbonestructure for it to be optimized by gradient descent.
To the best of our knowledge, no amortizedinference technique was proven to work with experimental datasets in a heterogeneous reconstructionsetting with unknown poses.
Our approach (cryoFIRE) uses a conditioned neural network to implicitly represent the conformationalspace V .
An encoder amortizes the inference of both z
i and ϕ i over the size of the dataset and adifferentiable rendering pipeline generates noise-free images.
In contrast to previous techniques thatjointly amortize the estimation of ϕ i and z i , cryoFIRE can perform heterogeneous reconstruction onexperimental datasets.
Methods
3.1 Image Formation Model
In single particle cryo-EM, probing electrons interact with the electrostatic potential created by themolecules embedded in a thin layer of vitreous ice (Figure 1 (a)).
During reconstruction, we assumethat this potential can be broken down into spatially bounded independent potentials ( volumes ) createdby individual molecules.
Each volume V i can be seen as a mapping from R 3 to R and is indexedby i ∈ { 1 , . .
. , N } .
We assume that the volumes { V i } i =1 ,...,N are drawn independently from aprobability distribution P V supported on a low-dimensional manifold (the conformational space )in the space F ( R 3 , R ) of all possible 3D potentials ( F ( A, B ) is the set of functions from A to B ).
More specifically, we assume there exist d ∈ N and V : R 3 × R d → R such that P V is supported onthe conformational space {V ( ., z ) , z ∈ R d } .
In the sample, each molecule is in an unknown orientation R i ∈
SO (3) ⊂ R 3 × 3 in the frame of theobserver.
The probing electron beam interacts with the electrostatic potential and its projections,
[Equation]
are considered mappings from R 2 to R .
The interaction between the beam and the lens is modeled bythe Point Spread Function (PSF) P i .
Imperfect centering of the molecule in the image is characterizedby small translations t i ∈
R 2 .
Finally, taking into account signal arising from the vitreous ice intowhich the molecules are embedded as well as the non-idealities of the lens and the detector, eachimage Y i is generally modeled as
[Equation]
where ∗ is the convolution operator, T t the t -translation kernel and η i white Gaussian noise on 156 R[36, 29].
The Fourier-Slice Theorem [4] (FST) avoids the computation of integrals and convolutions in Eq.
(2)and is also satisfied with the Hartley transform:
[Equation]
where H 2 D and H 3 D are the 2D and 3D Hartley transform operators [8] (sum of the real and imaginaryparts of the Fourier transform).
The “slice” operator S i is defined such that for any ˆ V : R 3 → R ,
[Equation]
Finally, if ˆ Y i =
H 2 D
[ Y i ] and ˆ V ( ., z i ) =
H 3 D
[ V ( ., z i )] , the image formation model in Hartley spacecan be expressed as
[Equation]
where ⊙ indicates element-wise multiplication,
C i
=
H 2 D [ P i ] is the Contrast Transfer Function [Figure]
3.2 Overview of cryoFIRE
Fig.
2 summarizes the architecture of cryoFIRE.
Images Y i are fed into an encoder, parameterized byψ , that predicts a pose ϕ
=
( R i , t i ) and a conformational state z i .
R i is used to rotate a grid of D 23D-coordinates in Hartley space.
These coordinates are concatenated with the conformational statebefore being fed into a neural representation of the function ˆ V θ (in Hartley space), parameterized by θ .ˆ
V θ is a mapping from R 3+ d to R and can be seen as a parametric representation of the conformationalspace in Hartley domain (a manifold of dimension d ).
Queried for all k in the grid, the neuralrepresentation outputs a set of real values corresponding to a discrete sampling of the slice definedin Eq.
Based on the estimated translation t i and given CTF parameters C i , the rest of theimage formation model described in Eq.
(5) is simulated to obtain ˆ X
i , a noise-free estimation ofˆ Y i .
The whole forward model is refered to as Γ ψ,θ , such that ˆ X i =
Γ ψ,θ ( Y i ) .
Pairs of measuredand reconstructed images are compared using the symmetric loss (see Section 3.5) and gradients arebackpropagated throughout the differentiable model in order to optimize both the encoder and theneural representation.
3.3 Discriminative Model
In cryoFIRE, an encoder acts as a discriminative model by mapping images to estimates of ϕ i and z i .
The encoder is structured sequentially with the following components:
A Convolutional Neural Network (CNN) containing 7 convolutional layers extracts highlevel visual features from images and divides the width and height of images by 32 .
Thearchitecture of the CNN is inspired from the first layers of VGG16 [31] , known
to performwell on visual tasks
A shared Multi-Layer Perceptron (MLP) with 2 hidden layers that outputs a feature y i ofdimension 256 .
A conformation MLP that maps y i to z i .
Rotation and translation MLPs that map the concatenation of y i and z i respectively to R
i
and t i .
The pose prediction is conditioned on z i since rotations and translations are onlydefined for a given conformation of the molecule and z i contains, with a small number ofdimensions, all the required information to determine the conformational state.
The rotationis represented in the 6-dimensional space S 2 × S 2 [42] as it was shown to lead to the bestresults for the rotation prediction in [21].
We experimented with both variational (predicting an approximate posterior distribution over latentvariables) and non-variational (predicting a point estimate) approaches and did not observe any significant performance difference (although the variational approach is more computationally expensive).
Full details about the architecture of the encoder are given in Supplement A.
3.4 Generative Model
The generative model is a simulation of the image formation model in Hartley space, in order tomake use of the FST (Section 3.1).
The forward pass is differentiable with respect to z i , R i and t i .
For each i , a grid of D 2 coordinates on the x-y plane in Hartley space are rotated by R i (mappedfrom S 2 × S 2 to R 3 × 3 using Gram–Schmidt orthogonalization) via a matrix multiplication.
Rotatedpoints k are positionally encoded with a bank of D/ 2 random frequencies [34] and independentlyconcatenated with the conformational state z
i before being fed into an MLP mapping R 3+ d to R .
This neural network is an implicit representation of the function ˆ V , where ˆ V ( ., z )
=
H 3 D
[ V ( ., z )] .
Additional implementation details about the neural network are given in Supplement B.
The CTF is defined by the defocus parameters and the astigmatism angle (provided by the simulatoror by an external software like CTFFIND [26] for experimental datasets).
It is then applied to theslice of size D 2 outputted by the neural representation.
Finally, the slice is element-wise multipliedby ˆ T t i , the Hartley transform of the t i -translation kernel.
3.5 Training Procedure
In the setting where poses are unknown, one cannot distinguish, given a set of 2D projections, twomolecules with different handedness.
This is called the “handedness ambiguity” [28].
Ref.
[17]showed that this leads amortized inference techniques to get stuck in local minima where the predictedmolecule contains spurious planar symmetries.
A solution suggested to alleviate this problem is touse the symmetric loss
[Equation]
(6) where B is a batch of indices and R π applies an in-plane rotation of π on images (we refer thereader to [17] for an ablation study on the symmetric loss and its instrumental role in the amortizedinference of poses).
In order to enable the model to converge to a consensus volume, we disable theoptimization of the conformation MLP at the start of the training.
During this “pose-only phase”, z iare randomly sampled from a normalized Gaussian distribution.
Results
We evaluate cryoFIRE for ab initio heterogeneous reconstruction and compare it with the state-ofthe-art method cryoDRGN2 [40].
We first validate that using an encoder to predict poses, insteadof performing an exhaustive pose search, enables us to reduce the runtime of heterogeneous reconstruction on a synthetic dataset.
We show that the encoder is able to accurately predict ϕ
i and z ifor images it has never processed during training, thereby validating the ability of an encoder-likearchitecture to amortize the runtime over the size of the dataset.
Secondly, we show that cryoFIREenables the detection of discrete heterogeneity in a dataset, by clustering images in the z i -space.
Finally, we show that our method can perform heterogeneous reconstruction of real data, a first for amethod that jointly amortizes the estimation of poses and conformations.
4.1 Runtime Improvement and Amortization
Experimental Setup We prepare three synthetic datasets of varying sizes – small (50k images),medium (500k images) and large (5M images) (Supplement C).
Images are generated using asimulation of the image formation model on ground truth volumes of the 80S ribosome.
Each datasetcontains a mix of projections with 90% sampled from the one of the volumes ( major ) and the restfrom the other volume ( minor ).
CTFs are drawn randomly with a log-normal distribution overthe defocus range.
We add Gaussian noise with variance σ 2 = 10 to the normalized projections(SNR= − 10 dB).
With cryoFIRE, we fix d = 8 and activate the conformation MLP after the model hasseen 1 .
5 M images.
We compare our method with cryoDRGN2 [40] with default parameters.
Pixels’intensities are set to 0 outside of a circle of radius 32 pixels for pose search.
With cryoDRGN2,pose search is done every 5 epochs for the small datasets and every epoch for the medium and largedatasets.
We train the models on a single NVIDIA A100 SXM4 40GB GPU.
Images of size D = 128are fed by batches of maximum sizes ( 128 for cryoFIRE, 32 for cryoDRGN2) and loaded on the fly [Table] using multi-threading on 16 CPUs.
The model is optimized with the ADAM optimizer [11] and alearning rate of 10 − 4 .
Convergence is detected by monitoring the pose prediction accuracy.
Onceconvergence is reached on the train set , latent variables can be estimated on a test set of 10k images,in order to validate that the encoder is not just memorizing the training set.
With cryoDRGN2, posesfrom the test set are estimated with a randomly-initialized pose search on the model obtained at traintime.
Metrics We compute the median and the mean of the angular error on the view direction, in degrees,and the median and mean square error of the predicted t i , in pixels.
Before computing pose errors, arigid 6D-body alignment is applied on the set of predicted poses to align the model into the sameglobal reference frame as the ground truth volume.
We perform a Principal Component Analysis(PCA) on the set of predicted
z i ’s and, looking at the first principal component, we group imagesin two classes, according to the cluster they fall into.
The confusion error is defined as the ratio ofmisclassified images over the total number of images.
After convergence, we generate two volumesby taking the centroids of the clusters in z i space and using them as inputs for the neural network ˆ V θon them.
We report the resolution (in pixels) obtained on the major ( 90% ) and on the minor ( 10% )volumes.
The reported resolution is the inverse of the maximum frequency for which the Fourier Shell Correlation is above 0 .
Results We report the runtime and quantitative metrics in Table 1.
At train time, the averagetime for processing one image is 19 ms (5:10h / ( 2 × 500 000 )) with cryoDRGN2 vs. 1 .
5 ms(1:28h / ( 7 × 500 000 ))
for cryoFIRE.
(The runtime of cryoDRGN2 is lower with the small datasetbecause pose search is only done every 5 epochs).
At test time, only the encoder of cryoFIRE isused, which further decreases the runtime per image ( 1 . 1 ms).
The accuracy obtained at test time onϕ i and z i validates that our method effectively amortizes the estimation of latent variables, and theerrors on the test sets decrease with the size of the dataset provided for training.
The accuracy ofpredicted poses is slightly worse with cryoFIRE than with an exhaustive pose search strategy (see
Supplement E for a comparison with a fully non-amortized method [25]).
The quantitative resolutionof the reconstructed volumes remains however very similar with both methods (see Supplement E fora qualitative comparison).
4.2 Heterogeneous Reconstruction of Synthetic Datasets
Experimental Setup We prepare three heterogeneous datasets of 100 k images of the Plasmodiumfalciparum 80S ribosome (Supplement C).
The three datasets contain an equal mix of projectionsfrom K ∈ { 2 , 3 , 10 } different ground truth volumes, generated sequentially along a reaction path
[Figure]
Results In Fig.
3, we plot the first principal component (PC1) of the set of z
i ’s vs. the ground truthindex of the volume each image was generated from.
With the dataset containing K conformations,images can be clustered in K groups, based on the value of PC1 ( K ∈ { 2 , 3 } ).
Looking for theoptimal thresholds on PC1, we compute a confusion error of 1 × 10 − 3 (resp.
2 × 10 − 2 ) on the 2 classes(resp.
3 classes ) dataset.
On the 10 classes dataset, the 10 conformations cannot be separated but thevalue of PC1 embeds information about the movement of the ribosome, as indicated by the Spearmancorrelation [14] between the index of the ground truth conformation and PC1.
Sampling differentvalues for PC1 (and setting the other components to zero), we can use the neural representation ˆ V θto generate a set of volumes from a set of conformational states z i .
Qualitative results are given in Fig.
3 (d), showing an accurate reconstruction of the movement of a subunit of the ribosome.
4.3 Heterogeneous Reconstruction of an Experimental Dataset
Experimental Setup We use the publicly available dataset EMPIAR-10180 [22] of a pre-catalyticspliceosome (Supplement C).
We run cryoFIRE with d = 8 , activate the conformation MLP after 30epochs and train for a total of 100 epochs.
Results from cryoDRGN2 [40] and cryoDRGN-BNB [39]on the same dataset are obtained from [40].
Results The first two components of a PCA on the set of predicted
z i ’s is shown in Fig.4.
Bytraversing the conformational space along the direction of PC1 and generating volumes on set of 5points, cryoFIRE generates a trajectory, showing a large flexing motion of the spliceosome.
CryoFIREqualitatively recovers the non-uniform distribution of viewing directions, avoids the local minimacryoDRGN-BNB falls into, and reconstructs volumes which qualitatively match the state of theart. See Supplement D for more results and a reconstruction on an experimental dataset of the 80Sribosome (EMPIAR-10028 [37]).
Discussion
As the resolving power of a sampling method scales with the size of the dataset, an increasing numberof images need to be collected in cryo-EM in order to extract meaningful structural information.
CryoFIRE answers the need for reconstruction methods that scale appropriately with the datasetsize: heterogeneous ab initio reconstruction on a dataset of 5M images can be performed within 2hours.
CryoFIRE is also the first reconstruction method to perform joint amortization of poses andconformations on an experimental cryo-EM dataset, opening the door to fast analysis of structuralheterogeneity on real datasets.
The interpretability of the conformational space remains an open question.
Since distances inthis space are not meaningful ( z i conditions the volume via a nonlinear decoder), the probabilitydistribution cannot be straightforwardly interpreted in that space. In the case of discrete heterogeneity, [Figure]
[Figure] [Figure] general quantities like the number of states or the relative populations of the states can be reliablyinferred from the conformational space by clustering the predicted conformational states.
In the caseof continuous heterogeneity, dimensionality reduction methods like PCA can highlight directionsof maximal variance and, by visual inspection of the reconstructed volumes, cryoFIRE can helpunderstanding the main degrees of freedom of a continuously deformable molecule.
However, “small”and “large” deformations can stem from similar changes in the conformational space and no physicallyinterpretable notion of distance is currently associated with the conformational space: providing thisspace with a physically interpretable metric is an interesting avenue for future work.
It is worth highlighting that the parameterization proposed here is not uniquely defined: a rotationof the molecule can equivalently be represented by R i or by a change of conformation state z i .
Empirically, cryoFIRE decorrelates poses and conformation by relying on a “pose-only phase” atthe beginning of training, but nothing explicitly prevents z i from containing information about R i .
Future work could explore improvements in the optimization procedure to further enforce minimalmutual information between poses and conformation.
Finally, we note that the accuracy of pose estimation (especially on translations) is lower withcryoFIRE than with exhaustive pose search methods.
Inaccurate translation prediction can lead to“blurry” reconstructions and therefore limits the resolution of reconstructed volumes.
This is a directreflection of the fact that amortization maximizes a non-tight lower-bound of the likelihood, allowingfor faster inference at the cost of accuracy [6].
Future work could investigate a hybrid approach thatwould estimate poses with an encoder at the beginning of training and switch, at the end, to a localpose search initialized from encoder-estimated poses.
Broader Impacts
Statement The cryo-EM field is generating data at a rapidly increasing pace,potentially leading to wasteful storage and inefficient computing.
The design of more efficientmethods such as CryoFIRE provides a path to mitigate sustainability risks.
In order to better comparemodern reconstruction methods, careful attention must be paid toward designing common datasetsand evaluation metrics.
By providing an open-source implementation of CryoFIRE upon publication,together with benchmark metrics, we hope to make cryo-EM research accessible to a broader classof researchers.
We also acknowledge that, by pushing further the boundaries of biological research,our method may facilitate the development of harmful biologics, however this is outweighed by itssignificant societal benefits, such as enabling antibody-vaccine development [1].
We encourage thecryo-EM community to play wisely with cryoFIRE.
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