Conformational Ensemble Research Articles

A novel framework for debris flow susceptibility assessment considering the uncertainty of sample selection

The uncertainty arising from random sampling of non-debris flow samples significantly impacts the accuracy of debris flow susceptibility assessments (DFSA). This study introduces a novel uncertainty elimination method, Kernel Density Estimation (KDE), and compares it with Mean and Maximum Probability Analysis (MPA) methods. Furthermore, we investigate the responses of four commonly used machine learning models to sampling uncertainty, comparing two structurally similar models (Random Forest (RF) and Extremely Randomized Trees (ERT)) with two structurally different models (Support Vector Machine (SVM) and Multilayer Perceptron (MLP)). The results indicate that the application of these uncertainty elimination methods can significantly enhance AUC values and zoning accuracy, with the KDE method outperforming the others. Specifically, the AUC values based on KDE for RF, ERT, SVM, and MLP are 0.995, 0.999, 0.999, and 0.853, respectively. The corresponding zoning accuracy for these models is 1.00, 1.00, 1.00, and 0.78, respectively. The study further reveals that the responses to sampling uncertainty vary by model architecture: RF, ERT, and SVM typically exhibit bimodal normal distributions, while the MLP model shows a unimodal distribution. Additionally, MLP is more sensitive to variations in negative samples, whereas RF and ERT are less affected due to the ensemble structure.

Integrating fast iterative filtering and ensemble neural network structure with attention mechanism for carbon price forecasting

Accurate carbon price forecasts are crucial for policymakers and enterprises to understand the dynamics of carbon price fluctuations, enabling them to formulate informed policies and investment strategies. However, due to the non-linear and non-stationary nature of carbon price, traditional models often struggle to achieve high prediction accuracy. To address this challenge, this study proposes a novel integrated prediction framework designed to enhance forecast accuracy. First, the carbon price series is decomposed into a series of smoother subsequences using fast iterative filtering (FIF). Subsequently, an integrated prediction model, AM-TCN-LSTM, is constructed, incorporating the attention mechanism (AM), temporal convolutional networks (TCN), and long short-term memory (LSTM) neural networks. The attention mechanism adaptively captures complex features from multiple factors, while the TCN-LSTM efficiently extracts temporal features from the sequences. Finally, the results from each subsequence are aggregated to generate the final prediction. Five carbon markets in china: Guangdong, Hubei, Shenzhen, Beijing, and Shanghai were selected to verify the validity of the proposed model. Various comparative models and evaluation metrics were employed to assess performance. The results demonstrate that: (1) the TCN-LSTM model achieves higher prediction accuracy compared to single models. (2) FIF is a more effective decomposition method with superior performance compared to EMD-based methods. (3) The proposed model exhibits the highest predictive capability, with MAE values of 0.0964, 0.1403, 1.9476, 2.0848, and 0.5029 for the five carbon markets, significantly outperforming comparison models. (4) The attention mechanism effectively captures the influence of multiple factors on carbon price, particularly within the short-term components.

Divergent roles of DRY and NPxxY motifs in selective activation of downstream signalling by the apelin receptor.

G protein-coupled receptors (GPCRs) serve as critical communication hubs, translating a wide range of extracellular signals into intracellular responses that govern numerous physiological processes. In class-A GPCRs, conserved motifs mediate conformational changes of the active states of the receptor, and signal transduction is achieved by selectively binding to Gα proteins and/or adapter protein, arrestin. Apelin receptor (APJR) is a class-A GPCR that regulates a wide range of intracellular signalling cascades in response to apelin and elabela peptide ligands. Understanding how conserved motifs within APJR mediate activation and signal specificity remains unexplored. This study focuses on the functional roles of the DRY and NPxxY motifs within APJR by analyzing their impact on downstream signaling pathways across the receptor's conformational ensembles. Our findings provide compelling evidence that mutations within the conserved DRY and NPxxY motifs of APJR significantly alter its conformational preferences where modification of DRY motif leads to abrogation of G-protein coupling and mutation of NPxxY motif causing abolition of β-arrestin-2 recruitment. These observations shed light on the importance of these motifs in APJR activation and its potential for functional selectivity, highlighting the role of DRY/NPxxY as conformational switches of APJR signalling.

The Conformational Space of the SARS-CoV-2 Main Protease Active Site Loops Is Determined by Ligand Binding and Interprotomer Allostery.

The main protease (Mpro) of SARS-CoV-2 is essential for viral replication and is, therefore, an important drug target. Here, we investigate two flexible loops in Mpro that play a role in catalysis. Using all-atom molecular dynamics simulations, we analyze the structural ensemble of Mpro in an apo state and substrate-bound state. We find that the flexible loops can adopt open, intermediate (partly open), and closed conformations in solution, which differs from the partially closed state observed in crystal structures of Mpro. When the loops are in closed or intermediate states, the catalytic residues are more likely to be in close proximity, which is crucial for catalysis. Additionally, we find that substrate binding to one protomer of the homodimer increases the frequency of intermediate states in the bound protomer while also affecting the structural propensity of the apo protomer's flexible loops. Using dynamic network analysis, we identify multiple allosteric pathways connecting the two active sites of the homodimer. Common to these pathways is an allosteric hotspot involving the N-terminus, a critical region that comprises part of the binding pocket. Taken together, the results of our simulation study provide detailed insight into the relationships between the flexible loops and substrate binding in a prime drug target for COVID-19.

Existence of symmetry-broken excited states in single and ensemble quantum ring structures

Existence of symmetry-broken excited states in single and ensemble quantum ring structures

Selective Protonation of Catalytic Dyad for γ-Secretase-Mediated Hydrolysis Revealed by Multiscale Simulations.

γ-Secretase plays a crucial role in producing disease-related amyloid-β proteins by cleaving the amyloid precursor protein (APP). The enzyme employs its catalytic dyad containing two aspartates (Asp257 and Asp385) to hydrolyze the substrate by a general acid-base catalytic mechanism, necessitating monoprotonation of the two aspartates for efficient hydrolysis. However, the precise protonation states of the aspartates remain uncertain. In this study, we employed a multiscale computational approach to investigate the dependence of the catalytic efficiency of γ-secretase on the protonation states of its catalytic dyad. Over 200 ms unbiased atomistic simulations of the substrate-enzyme complex reveal diverse orientations of the scissile bond of the bound substrate and accessible structural ensembles of the catalytic dyad with Asp257-Asp385 distances fluctuating between 4 and 10 Å. With a quantum mechanics/molecular mechanics (QM/MM) approach accelerated by enhanced sampling techniques, we find that the first step of the hydrolysis reaction, i.e., the formation of a gem-diol intermediate, experiences a higher reaction barrier by ∼2 kcal/mol when Asp385 is protonated. Furthermore, we find that Arg269 of the enzyme is most likely responsible for this preference of the protonation state: its basic side chain is spatially close to that of Asp257 and specifically stabilizes the transition state electrostatically when Asp257 is protonated. Collectively, our study suggests that Asp257 is likely the favored protonation site for APP cleavage by γ-secretase.

SEC-SAXS/MC Ensemble Structural Studies of the Microtubule Binding Protein Cdt1 Show Monomeric, Folded-Over Conformations.

Cdt1 is a mixed folded protein critical for DNA replication licensing and it also has a "moonlighting" role at the kinetochore via direct binding to microtubules and the Ndc80 complex. However, it is unknown how the structure and conformations of Cdt1 could allow it to participate in these multiple, unique sets of protein complexes. While robust methods exist to study entirely folded or unfolded proteins, structure-function studies of combined, mixed folded/disordered proteins remain challenging. In this work, we employ orthogonal biophysical and computational techniques to provide structural characterization of mitosis-competent human Cdt1. Thermal stability analyses shows that both folded winged helix domains1 are unstable. CD and NMR show that the N-terminal and linker regions are intrinsically disordered. DLS shows that Cdt1 is monomeric and polydisperse, while SEC-MALS confirms that it is monomeric at high concentrations, but without any apparent inter-molecular self-association. SEC-SAXS enabled computational modeling of the protein structures. Using the program SASSIE, we performed rigid body Monte Carlo simulations to generate a conformational ensemble of structures. We observe that neither fully extended nor extremely compact Cdt1 conformations are consistent with SAXS. The best-fit models have the N-terminal and linker disordered regions extended into the solution and the two folded domains close to each other in apparent "folded over" conformations. We hypothesize the best-fit Cdt1 conformations could be consistent with a function as a scaffold protein that may be sterically blocked without binding partners. Our study also provides a template for combining experimental and computational techniques to study mixed-folded proteins.

Neural Thermodynamic Integration: Free Energies from Energy-Based Diffusion Models.

Thermodynamic integration (TI) offers a rigorous method for estimating free-energy differences by integrating over a sequence of interpolating conformational ensembles. However, TI calculations are computationally expensive and typically limited to coupling a small number of degrees of freedom due to the need to sample numerous intermediate ensembles with sufficient conformational-space overlap. In this work, we propose to perform TI along an alchemical pathway represented by a trainable neural network, which we term Neural TI. Critically, we parametrize a time-dependent Hamiltonian interpolating between the interacting and noninteracting systems and optimize its gradient using a score matching objective. The ability of the resulting energy-based diffusion model to sample all intermediate ensembles allows us to perform TI from a single reference calculation. We apply our method to Lennard-Jones fluids, where we report accurate calculations of the excess chemical potential, demonstrating that Neural TI reproduces the underlying changes in free energy without the need for simulations at interpolating Hamiltonians.

SOP-MULTI: A Self-Organized Polymer-Based Coarse-Grained Model for Multidomain and Intrinsically Disordered Proteins with Conformation Ensemble Consistent with Experimental Scattering Data.

Multidomain proteins with long flexible linkers and full-length intrinsically disordered proteins (IDPs) are best defined as an ensemble of conformations rather than a single structure. Determining high-resolution ensemble structures of such proteins poses various challenges by using tools from experimental structural biophysics. Integrative approaches combining available low-resolution ensemble-averaged experimental data and in silico biomolecular reconstructions are now often used for the purpose. However, extensive Boltzmann weighted conformation sampling for large proteins, especially for ones where both the folded and disordered domains exist in the same polypeptide chain, remains a challenge. In this work, we present a 2-site per amino-acid resolution SOP-MULTI force field for simulating coarse-grained models of multidomain proteins. SOP-MULTI combines two well-established self-organized polymer models─: (i) SOP-SC models for folded systems and (ii) SOP-IDP for IDPs. For the SOP-MULTI, we introduce cross-interaction terms between the beads belonging to the folded and disordered regions to generate conformation ensembles for full-length multidomain proteins such as hnRNP A1, TDP-43, G3BP1, hGHR-ECD, TIA1, HIV-1 Gag, polyubiquitin, and FUS. When back-mapped to all-atom resolution, SOP-MULTI trajectories faithfully recapitulate the scattering data over the range of the reciprocal space. We also show that individual folded domains preserve native contacts with respect to solved folded structures, and root-mean-square fluctuations of residues in folded domains match those obtained from all-atom molecular dynamics simulation trajectories of the same folded systems. SOP-MULTI force field is made available as a LAMMPS-compatible user package along with setup codes for generating the required files for any full-length protein with folded and disordered regions.

CACHE Challenge #1: Targeting the WDR Domain of LRRK2, A Parkinson's Disease Associated Protein.

The CACHE challenges are a series of prospective benchmarking exercises to evaluate progress in the field of computational hit-finding. Here we report the results of the inaugural CACHE challenge in which 23 computational teams each selected up to 100 commercially available compounds that they predicted would bind to the WDR domain of the Parkinson's disease target LRRK2, a domain with no known ligand and only an apo structure in the PDB. The lack of known binding data and presumably low druggability of the target is a challenge to computational hit finding methods. Of the 1955 molecules predicted by participants in Round 1 of the challenge, 73 were found to bind to LRRK2 in an SPR assay with a KD lower than 150 μM. These 73 molecules were advanced to the Round 2 hit expansion phase, where computational teams each selected up to 50 analogs. Binding was observed in two orthogonal assays for seven chemically diverse series, with affinities ranging from 18 to 140 μM. The seven successful computational workflows varied in their screening strategies and techniques. Three used molecular dynamics to produce a conformational ensemble of the targeted site, three included a fragment docking step, three implemented a generative design strategy and five used one or more deep learning steps. CACHE #1 reflects a highly exploratory phase in computational drug design where participants adopted strikingly diverging screening strategies. Machine learning-accelerated methods achieved similar results to brute force (e.g., exhaustive) docking. First-in-class, experimentally confirmed compounds were rare and weakly potent, indicating that recent advances are not sufficient to effectively address challenging targets.

Oxygen Vacancy-Electron Polarons Featured InSnRuO2 Oxides: Orderly and Concerted In-Ov-Ru-O-Sn Substructures for Acidic Water Oxidation.

Polymetallic oxides with extraordinary electrons/geometry structure ensembles, trimmed electron bands, and way-out coordination environments, built by an isomorphic substitution strategy, may create unique contributing to concertedly catalyze water oxidation, which is of great significance for proton exchange membrane water electrolysis (PEMWE). Herein, well-defined rutile InSnRuO2 oxides with density-controllable oxygen vacancy (Ov)-free electron polarons are firstly fabricated by in situ isomorphic substitution, using trivalent In species as Ov generators and the adjacent metal ions as electron donors to form orderly and concerted In-Ov-Ru-O-Sn substructures in the tetravalent oxides. For acidic water oxidation, the obtained InSnRuO2 displays an ultralow overpotential of 183 mV (versus RHE) and a mass activity (MA) of 103.02 A mgRu -1, respectively. For a long-term stability test of PEMWE, it can run at a low and unchangeable cell potential (1.56 V) for 200 h at 50 mA cm-2, far exceeding current IrO2||Pt/C assembly in 0.5 m H2SO4. Accelerated degradation testing results of PEMWE with pure water as the electrolyte show no significant increase in voltage even when the voltage is gradually increased from 1 to 5 A cm-2. The remarkably improved performance is associated with the concerted In-Ov-Ru-O-Sn substructures stabilized by the dense Ov-electron polarons, which synergistically activates band structure of oxygen species and adjacent Ru sites and then boosting the oxygen evolution kinetics. More importantly, the self-trapped Ov-electron polaron induces a decrease in the entropy and enthalpy, and efficiently hinder Ru atoms leaching by increasing the lattice atom diffusion energy barrier, achieves long-term stability of the oxide. This work may open a door to design next-generation Ru-based catalysts with polarons to create orderly and asymmetric substructures as active sites for efficient electrocatalysis in PEMWE application.

Unraveling the impact of mutations on the functional dynamics, stability, and energetics of dengue virus non-structural protein 1

ABSTRACT The non-structural protein 1 (NS1), a viral toxin, is linked to serious consequences of dengue. Given its crucial role in the viral life cycle, NS1 has been a primary target for antiviral drug development. This study elucidates the mechanistic impact of specific NS1 mutations, V220D and A248V, identified by Tan and colleagues as potential inhibitors of viral replication. We developed an integrated computational framework to analyze these mutations relative to the native NS1 protein. Using conventional all-atom molecular dynamic simulations followed by site-directed in silico mutagenesis, significant alterations in protein structure were observed. Conformational ensembles over time showed average backbone deviations of 0.44 nm and 0.43 nm for V220D and A248V, respectively, compared to 0.37 nm for the wild type. Residue-wise fluctuations were higher in A248V compared to both wild type and V220D systems. Mutation-induced disruptions in the hydrogen bond network and altered protein structure graphs were also revealed. Principal component analysis and free energy landscape assessments showed the wild-type protein had a more constrained and stable conformation, whereas the mutants displayed scattered energy contours, suggesting reduced structural stability. This comprehensive assessment provides deep insight into the structural impact of NS1 mutations, informing future efforts in antiviral drug development targeting NS1.

Molecular Modeling of Glycosylated Catalytic Domain of Human Carbonic Anhydrase IX.

Glycans exhibit significant structural diversity due to the flexibility of glycosidic bonds linking their constituent monosaccharides and the formation of numerous hydrogen bonds. The present work searches a simulated ensemble of glycan chain conformations attached to the catalytic domain of N-glycosylated human carbonic anhydrase IX (HCA IX-c) to identify conformations pointed away or back-folded toward the protein surface guided by different amino acid residues. A series of classical molecular dynamics (MD) simulation studies for a total of 30 μs followed by accelerated MD simulations for a total of 2 μs have been performed using two different force fields to capture varying degrees of fluctuations of both glycan chain and HCA IX. From the underlying free energy profile and kinetics derived using hidden Markov state model, several stable glycan orientations are identified that extend away from the protein surface and convert among each other with rate constants of the order 107-1010 S-1. Most importantly, we have identified a rare glycan conformation which reaches close to a catalytically important amino acid residue, Glu-106. We further enlist the protein residues that couple such less frequent event of the glycan chain back-folding toward the surface of the protein.

Probing Functional Allosteric States and Conformational Ensembles of the Allosteric Protein Kinase States and Mutants: Atomistic Modeling and Comparative Analysis of AlphaFold2, OmegaFold, and AlphaFlow Approaches and Adaptations.

This study reports a comprehensive analysis and comparison of several AlphaFold2 adaptations and OmegaFold and AlphaFlow approaches in predicting distinct allosteric states, conformational ensembles, and mutation-induced structural effects for a panel of state-switching allosteric ABL mutants. The results revealed that the proposed AlphaFold2 adaptation with randomized alanine sequence scanning can generate functionally relevant allosteric states and conformational ensembles of the ABL kinase that qualitatively capture a unique pattern of population shifts between the active and inactive states in the allosteric ABL mutants. Consistent with the NMR experiments, the proposed AlphaFold2 adaptation predicted that G269E/M309L/T408Y mutant could induce population changes and sample a significant fraction of the fully inactive I2 form which is a low-populated, high-energy state for the wild-type ABL protein. We also demonstrated that other ABL mutants G269E/M309L/T334I and M309L/L320I/T334I that introduce a single activating T334I mutation can reverse equilibrium and populate exclusively the active ABL form. While the precise quantitative predictions of the relative populations of the active and various hidden inactive states in the ABL mutants remain challenging, our results provide evidence that AlphaFold2 adaptation with randomized alanine sequence scanning can adequately detect a spectrum of the allosteric ABL states and capture the equilibrium redistributions between structurally distinct functional ABL conformations. We further validated the robustness of the proposed AlphaFold2 adaptation for predicting the unique inactive architecture of the BSK8 kinase and structural differences between ligand-unbound apo and ATP-bound forms of BSK8. The results of this comparative study suggested that AlpahFold2, OmegaFold, and AlphaFlow approaches may be driven by structural memorization of existing protein folds and are strongly biased toward predictions of the thermodynamically stable ground states of the protein kinases, highlighting limitations and challenges of AI-based methodologies in detecting alternative functional conformations, accurate characterization of physically significant conformational ensembles, and prediction of mutation-induced allosteric structural changes.

Phosphorylation of disordered proteins tunes local and global intramolecular interactions.

Protein post-translational modifications, such as phosphorylation, are important regulatory signals for diverse cellular functions. In particular, intrinsically disordered protein regions (IDRs) are subject to phosphorylation as a means to modulate their interactions and functions. Toward understanding the relationship between phosphorylation in IDRs and specific functional outcomes, we must consider how phosphorylation affects the IDR conformational ensemble. Various experimental techniques are suited to interrogate the features of IDR ensembles; molecular simulations can provide complementary insights and even illuminate ensemble features that may be experimentally inaccessible. Therefore, we sought to expand the tools available to study phosphorylated IDRs by all-atom Monte Carlo simulations. To this end, we implemented parameters for phosphoserine (pSer) and phosphothreonine (pThr) into the OPLS version of the continuum solvent model, ABSINTH, and assessed their performance in all-atom simulations compared to published findings. We simulated short (< 20 residues) and long (> 80 residues) phospho-IDRs that, collectively, survey both local and global phosphorylation-induced changes to the ensemble. Our simulations of four well-studied phospho-IDRs show near-quantitative agreement with published findings for these systems via metrics including changes to radius of gyration, transient helicity, and persistence length. We also leveraged the inherent advantage of sequence control in molecular simulations to explore the conformational effects of diverse combinations of phospho-sites in two multi-phosphorylated IDRs. Our results support and expand on prior observations that connect phosphorylation to changes in the IDR conformational ensemble. Herein, we describe phosphorylation as a means to alter sequence chemistry, net charge and charge patterning, and intramolecular interactions, which can collectively modulate the local and global IDR ensemble features.

Assessing small molecule conformational sampling methods in molecular docking.

Small molecule conformational sampling plays a pivotal role in molecular docking. Recent advancements have led to the emergence of various conformational sampling methods, each employing distinct algorithms. This study investigates the impact of different small molecule conformational sampling methods in molecular docking using UCSF DOCK 3.7. Specifically, six traditional sampling methods (Omega, BCL::Conf, CCDC Conformer Generator, ConfGenX, Conformator, RDKit ETKDGv3) and a deep learning-based model (Torsional Diffusion) for generating conformational ensembles are evaluated. These ensembles are subsequently docked against the Platinum Diverse Dataset, the PoseBusters dataset and the DUDE-Z dataset to assess binding pose reproducibility and screening power. Notably, different sampling methods exhibit varying performance due to their unique preferences, such as dihedral angle sampling ranges on rotatable bonds. Combining complementary methods may lead to further improvements in docking performance.

The fuzzy Potts model in the plane: scaling limits and arm exponents

AbstractWe consider a critical Fortuin–Kasteleyn (FK) percolation with cluster weight $$q \in [1,4)$$ q ∈ [ 1 , 4 ) in the plane, and color its clusters in red (respectively blue) with probability $$r \in (0,1)$$ r ∈ ( 0 , 1 ) (respectively $$1-r$$ 1 - r ), independently of each other. We study the resulting fuzzy Potts model, which corresponds to the critical Ising model in the special case $$q=2$$ q = 2 and $$r=1/2$$ r = 1 / 2 . We show that under the assumption that the critical FK percolation converges to a conformally invariant scaling limit (which is known to hold for the FK-Ising model,i.e. $$q=2$$ q = 2 ), the obtained coloring converges to variants of Conformal Loop Ensembles constructed, described and studied by Miller, Sheffield and Werner. Based on discrete considerations, we also show that the arm exponents for this coloring in the discrete model are identical to the ones of the continuum model. Using the values of these arm exponents in the continuum, we determine the arm exponents for the fuzzy Potts model.

Impact of Phosphorylation on the Physiological Form of Human alpha-Synuclein in Aqueous Solution.

Serine 129 can be phosphorylated in pathological inclusions formed by the intrinsically disordered protein human α-synuclein (AS), a key player in Parkinson's disease and other synucleinopathies. Here, molecular simulations provide insight into the structural ensemble of phosphorylated AS. The simulations allow us to suggest that phosphorylation significantly impacts the structural content of the physiological AS conformational ensemble in aqueous solution, as the phosphate group is mostly solvated. The hydrophobic region of AS contains β-hairpin structures, which may increase the propensity of the protein to undergo amyloid formation, as seen in the nonphysiological (nonacetylated) form of the protein in a recent molecular simulation study. Our findings are consistent with existing experimental data with the caveat of the observed limitations of the force field for the phosphorylated moiety.

Asymmetric fluctuation of overlapping dinucleosome studied by cryoelectron microscopy and small-angle X-ray scattering.

Nucleosome remodelers modify the local structure of chromatin to release the region from nucleosome-mediated transcriptional suppression. Overlapping dinucleosomes (OLDNs) are nucleoprotein complexes formed around transcription start sites as a result of remodeling, and they consist of two nucleosome moieties: a histone octamer wrapped by DNA (octasome) and a histone hexamer wrapped by DNA (hexasome). While OLDN formation alters chromatin accessibility to proteins, the structural mechanism behind this process is poorly understood. Thus, this study investigated the characteristics of structural fluctuations in OLDNs. First, multiple structures of the OLDN were visualized through cryoelectron microscopy (cryoEM), providing an overview of the tilting motion of the hexasome relative to the octasome at the near-atomistic resolution. Second, small-angle X-ray scattering (SAXS) revealed the presence of OLDN conformations with a larger radius of gyration than cryoEM structures. A more complete description of OLDN fluctuation was proposed by SAXS-based ensemble modeling, which included possible transient structures. The ensemble model supported the tilting motion of the OLDN outlined by the cryoEM models, further suggesting the presence of more diverse conformations. The amplitude of the relative tilting motion of the hexasome was larger, and the nanoscale fluctuation in distance between the octasome and hexasome was also proposed. The cryoEM models were found to be mapped in the energetically stable region of the conformational distribution of the ensemble. Exhaustive complex modeling using all conformations that appeared in the structural ensemble suggested that conformational and motional asymmetries of the OLDN result in asymmetries in the accessibility of OLDN-binding proteins.

Bayesian electron density determination from sparse and noisy single-molecule X-ray scattering images.

Single molecule x-ray scattering experiments using free-electron lasers hold the potential to resolve biomolecular structures and structural ensembles. However, molecular electron density determination has so far not been achieved because of low photon counts, high noise levels, and low hit rates. Most approaches therefore focus on large specimen like entire viruses, which scatter sufficiently many photons to allow orientation determination of each image. Small specimens like proteins, however, scatter too few photons for the molecular orientations to be determined. Here, we present a rigorous Bayesian approach to overcome these limitations, additionally taking into account intensity fluctuations, beam polarization, irregular detector shapes, incoherent scattering, and background scattering. We demonstrate using synthetic scattering images that electron density determination of small proteins is possible in this extreme high noise Poisson regime. Tests on published virus data achieved the detector-limited resolution of 9 nm, using only 0.01% of the available photons per image.